当前期刊: "综合"类期刊
显示样式:        排序: 导出
我的关注
我的收藏
您暂时未登录!
登录
  • Pair correlation of sequences $(\lbrace a_n \alpha \rbrace)_{n \in {\mathbb N}}$ with maximal additive energy
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-09-06
    GERHARD LARCHER; WOLFGANG STOCKINGER

    We show for sequences $\left(a_{n}\right)_{n \in \mathbb N}$ of distinct positive integers with maximal order of additive energy, that the sequence $\left(\left\{a_{n} \alpha\right\}\right)_{n \in \mathbb N}$ does not have Poissonian pair correlations for any α. This result essentially sharpens a result obtained by J. Bourgain on this topic.

    更新日期:2020-02-18
  • Local rings with quasi-decomposable maximal ideal
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-09-26
    SAEED NASSEH; RYO TAKAHASHI

    Let (R, 𝔪) be a commutative noetherian local ring. In this paper, we prove that if 𝔪 is decomposable, then for any finitely generated R-module M of infinite projective dimension 𝔪 is a direct summand of (a direct sum of) syzygies of M. Applying this result to the case where 𝔪 is quasi-decomposable, we obtain several classifications of subcategories, including a complete classification of the thick subcategories of the singularity category of R.

    更新日期:2020-02-18
  • Elliptic Curves in Hyper-Kähler Varieties
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-14
    Nesterov D, Oberdieck G.

    We show that the moduli space of elliptic curves of minimal degree in a general Fano variety of lines of a cubic four-fold is a non-singular curve of genus $631$. The curve admits a natural involution with connected quotient. We find that the general Fano contains precisely $3,780$ elliptic curves of minimal degree with fixed (general) $j$-invariant. More generally, we express (modulo a transversality result) the enumerative count of elliptic curves of minimal degree in hyper-Kähler varieties with fixed $j$-invariant in terms of Gromov–Witten invariants. In $K3^{[2]}$-type this leads to explicit formulas of these counts in terms of modular forms.

    更新日期:2020-02-18
  • Example of Compact Special Lagrangians with a Stable Singularity
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-17
    Imagi Y.

    We construct a family of compact almost Calabi–Yau manifolds of complex dimension 3 and therein a corresponding family of compact special Lagrangians with one-point singularities modelled upon that $T^2$-cone constructed by Harvey and Lawson [7, Chapter III.3.A, Theorem 3.1] and characterised by Haskins [8, Theorem A] as a stable $T^2$-cone in the terminology by Joyce [16, Definition 3.4 and Example 3.5].

    更新日期:2020-02-18
  • Integral Hasse Principle and Strong Approximation for Markoff Surfaces
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-17
    Loughran D, Mitankin V.

    We study the failure of the integral Hasse principle and strong approximation for Markoff surfaces, as studied by Ghosh and Sarnak, using the Brauer–Manin obstruction.

    更新日期:2020-02-18
  • Gonality of dynatomic curves and strong uniform boundedness of preperiodic points
    Compos. Math. (IF 1.301) Pub Date : 2020-02-17
    John R. Doyle; Bjorn Poonen

    Fix $d\geqslant 2$ and a field $k$ such that $\operatorname{char}k\nmid d$ . Assume that $k$ contains the $d$ th roots of $1$ . Then the irreducible components of the curves over $k$ parameterizing preperiodic points of polynomials of the form $z^{d}+c$ are geometrically irreducible and have gonality tending to $\infty$ . This implies the function field analogue of the strong uniform boundedness conjecture for preperiodic points of $z^{d}+c$ . It also has consequences over number fields: it implies strong uniform boundedness for preperiodic points of bounded eventual period, which in turn reduces the full conjecture for preperiodic points to the conjecture for periodic points. Our proofs involve a novel argument specific to finite fields, in addition to more standard tools such as the Castelnuovo–Severi inequality.

    更新日期:2020-02-18
  • Deformation spaces and normal forms around transversals
    Compos. Math. (IF 1.301) Pub Date : 2020-02-17
    Francis Bischoff; Henrique Bursztyn; Hudson Lima; Eckhard Meinrenken

    Given a manifold $M$ with a submanifold $N$ , the deformation space ${\mathcal{D}}(M,N)$ is a manifold with a submersion to $\mathbb{R}$ whose zero fiber is the normal bundle $\unicode[STIX]{x1D708}(M,N)$ , and all other fibers are equal to $M$ . This article uses deformation spaces to study the local behavior of various geometric structures associated with singular foliations, with $N$ a submanifold transverse to the foliation. New examples include $L_{\infty }$ -algebroids, Courant algebroids, and Lie bialgebroids. In each case, we obtain a normal form theorem around $N$ , in terms of a model structure over $\unicode[STIX]{x1D708}(M,N)$ .

    更新日期:2020-02-18
  • Singular Curves of Low Degree and Multifiltrations from Osculating Spaces
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-10
    Buczyński J, Ilten N, Ventura E.

    In order to study projections of smooth curves, we introduce multifiltrations obtained by combining flags of osculating spaces. We classify all configurations of singularities occurring for a projection of a smooth curve embedded by a complete linear system away from a projective linear space of dimension at most two. In particular, we determine all configurations of singularities of non-degenerate degree $d$ rational curves in $\mathbb{P}^n$ when $d-n\leq 3$ and $d<2n$. Along the way, we describe the Schubert cycles giving rise to these projections. We also reprove a special case of the Castelnuovo bound using these multifiltrations: under the assumption $d<2n$, the arithmetic genus of any non-degenerate degree $d$ curve in $\mathbb{P}^n$ is at most $d-n$.

    更新日期:2020-02-13
  • The algebraic dimension of compact complex threefolds with vanishing second Betti number
    Compos. Math. (IF 1.301) Pub Date : 2020-02-13
    Frédéric Campana; Jean-Pierre Demailly; Thomas Peternell

    We study compact complex three-dimensional manifolds with vanishing second Betti number. In particular, we show that a compact complex manifold homeomorphic to the six-dimensional sphere does carry any non-constant meromorphic function.

    更新日期:2020-02-13
  • Additive correlation and the inverse problem for the large sieve
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-07-09
    BRANDON HANSON

    Let A ⊆ [1, N] be a set of integers with |A| ≫ $\sqrt N$ . We show that if A avoids about p/2 residue classes modulo p for each prime p, then A must correlate additively with the squares S = {n2 : 1 ≤ n ≤ $\sqrt N$ }, in the sense that we have the additive energy estimate $$ E(A,S)\gg N\log N. $$ This is, in a sense, optimal.

    更新日期:2020-02-11
  • On the Saxl graph of a permutation group
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-08-08
    TIMOTHY C. BURNESS; MICHAEL GIUDICI

    Let G be a permutation group on a set Ω. A subset of Ω is a base for G if its pointwise stabiliser in G is trivial. In this paper we introduce and study an associated graph Σ(G), which we call the Saxl graph of G. The vertices of Σ(G) are the points of Ω, and two vertices are adjacent if they form a base for G. This graph encodes some interesting properties of the permutation group. We investigate the connectivity of Σ(G) for a finite transitive group G, as well as its diameter, Hamiltonicity, clique and independence numbers, and we present several open problems. For instance, we conjecture that if G is a primitive group with a base of size 2, then the diameter of Σ(G) is at most 2. Using a probabilistic approach, we establish the conjecture for some families of almost simple groups. For example, the conjecture holds when G = Sn or An (with n > 12) and the point stabiliser of G is a primitive subgroup. In contrast, we can construct imprimitive groups whose Saxl graph is disconnected with arbitrarily many connected components, or connected with arbitrarily large diameter.

    更新日期:2020-02-11
  • Remarks on Wolff's inequality for hypersurfaces
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-09-06
    SHAOMING GUO; CHANGKEUN OH

    We run an iteration argument due to Pramanik and Seeger, to provide a proof of sharp decoupling inequalities for conical surfaces and for k-cones. These are extensions of results of Łaba and Pramanik to sharp exponents.

    更新日期:2020-02-11
  • On orbifold constructions associated with the Leech lattice vertex operator algebra
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-09-05
    CHING HUNG LAM; HIROKI SHIMAKURA

    In this paper, we study orbifold constructions associated with the Leech lattice vertex operator algebra. As an application, we prove that the structure of a strongly regular holomorphic vertex operator algebra of central charge 24 is uniquely determined by its weight one Lie algebra if the Lie algebra has the type A3,43A1,2, A4,52, D4,12A2,6, A6,7, A7,4A1,13, D5,8A1,2 or D6,5A1,12 by using the reverse orbifold construction. Our result also provides alternative constructions of these vertex operator algebras (except for the case A6,7) from the Leech lattice vertex operator algebra.

    更新日期:2020-02-11
  • Classification of the real discrete specialisations of the Burau representation of B3
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-10-09
    NANCY SCHERICH

    This classification is found by analyzing the action of a normal subgroup of B3 as hyperbolic isometries. This paper gives an example of an unfaithful specialisation of the Burau representation on B4 that is faithful when restricted to B3, as well as examples of unfaithful specialisations of B3.

    更新日期:2020-02-11
  • The frame of smashing tensor-ideals
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-10-19
    PAUL BALMER; HENNING KRAUSE; GREG STEVENSON

    We prove that every flat tensor-idempotent in the module category Mod- of a tensor-triangulated category comes from a unique smashing ideal in . We deduce that the lattice of smashing ideals forms a frame.

    更新日期:2020-02-11
  • The structure of triple homomorphisms onto prime algebras
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-10-23
    CHENG–KAI LIU

    Triple homomorphisms on C*-algebras and JB*-triples have been studied in the literature. From the viewpoint of associative algebras, we characterise the structure of triple homomorphisms from an arbitrary ⋆-algebra onto a prime *-algebra. As an application, we prove that every triple homomorphism from a Banach ⋆-algebra onto a prime semisimple idempotent Banach *-algebra is continuous. The analogous results for prime C*-algebras and standard operator *-algebras on Hilbert spaces are also described.

    更新日期:2020-02-11
  • Rational discrete first degree cohomology for totally disconnected locally compact groups
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-10-12
    ILARIA CASTELLANO

    It is well known that the existence of more than two ends in the sense of J.R. Stallings for a finitely generated discrete group G can be detected on the cohomology group H1(G,R[G]), where R is either a finite field, the ring of integers or the field of rational numbers. It will be shown (cf. Theorem A*) that for a compactly generated totally disconnected locally compact group G the same information about the number of ends of G in the sense of H. Abels can be provided by dH1(G, Bi(G)), where Bi(G) is the rational discrete standard bimodule of G, and dH•(G, _) denotes rational discrete cohomology as introduced in [6].

    更新日期:2020-02-11
  • Sequences, modular forms and cellular integrals
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-10-11
    DERMOT McCARTHY; ROBERT OSBURN; ARMIN STRAUB

    It is well-known that the Apéry sequences which arise in the irrationality proofs for ζ(2) and ζ(3) satisfy many intriguing arithmetic properties and are related to the pth Fourier coefficients of modular forms. In this paper, we prove that the connection to modular forms persists for sequences associated to Brown's cellular integrals and state a general conjecture concerning supercongruences.

    更新日期:2020-02-11
  • A group version of stable regularity
    Math. Proc. Camb. Philos. Soc. (IF 0.737) Pub Date : 2018-10-24
    G. CONANT; A. PILLAY; C. TERRY

    We prove that, given ε > 0 and k ≥ 1, there is an integer n such that the following holds. Suppose G is a finite group and A ⊆ G is k-stable. Then there is a normal subgroup H ≤ G of index at most n, and a set Y ⊆ G, which is a union of cosets of H, such that |A △ Y| ≤ε|H|. It follows that, for any coset C of H, either |C ∩ A|≤ ε|H| or |C \ A| ≤ ε |H|. This qualitatively generalises recent work of Terry and Wolf on vector spaces over $\mathbb{F}_p$ .

    更新日期:2020-02-11
  • 更新日期:2020-02-11
  • 更新日期:2020-02-11
  • GRADIENT AND HESSIAN ESTIMATES FOR DIRICHLET AND NEUMANN EIGENFUNCTIONS
    Q. J. Math. (IF 0.636) Pub Date : 2020-02-10
    Wang F.

    We establish integral formulas and sharp two-sided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, sharp gradient and Hessian estimates are derived for the Dirichlet and Neumann eigenfunctions.

    更新日期:2020-02-10
  • Densities of Currents on Non-Kähler Manifolds
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-10
    Vu D.

    We give a natural generalization of the Dinh–Sibony notion of density currents in the setting where the ambient manifold is not necessarily Kähler. As an application, we show that the algebraic entropy of meromorphic self-maps of compact complex surfaces is a finite bi-meromorphic invariant.

    更新日期:2020-02-10
  • Diophantine Property of Matrices and Attractors of Projective Iterated Function Systems in ℝℙ1
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-10
    Solomyak B, Takahashi Y.

    We prove that almost every finite collection of matrices in $GL_d( \mathbb{R} )$ and $SL_d({\mathbb{R}})$ with positive entries is Diophantine. Next we restrict ourselves to the case $d=2$. A finite set of $SL_2({\mathbb{R}})$ matrices induces a (generalized) iterated function system on the projective line ${\mathbb{RP}}^1$. Assuming uniform hyperbolicity and the Diophantine property, we show that the dimension of the attractor equals the minimum of 1 and the critical exponent.

    更新日期:2020-02-10
  • Sonine Formulas and Intertwining Operators in Dunkl Theory
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-09
    Rösler M, Voit M.

    Let $V_k$ denote Dunkl’s intertwining operator associated with some root system $R$ and multiplicity $k$. For two multiplicities $k, k^{\prime }$ on $R$, we study the intertwiner $V_{k^{\prime },k} = V_{k^{\prime }}\circ V_k^{-1}$ between Dunkl operators with multiplicities $k$ and $k^{\prime }.$ It has been a long-standing conjecture that $V_{k^{\prime },k}$ is positive if $k^{\prime } \geq k \geq 0.$ We disprove this conjecture by constructing counterexamples for root system $B_n$. This matter is closely related to the existence of Sonine-type integral representations between Dunkl kernels and Bessel functions with different multiplicities. In our examples, such Sonine formulas do not exist. As a consequence, we obtain necessary conditions on Sonine formulas for Heckman–Opdam hypergeometric functions of type $BC_n$ and conditions for positive branching coefficients between multivariable Jacobi polynomials.

    更新日期:2020-02-10
  • A Basis of Casimirs in 3D Magnetohydrodynamics
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-09
    Khesin B, Peralta-Salas D, Yang C.

    We prove that any regular Casimir in 3D magnetohydrodynamics (MHD) is a function of the magnetic helicity and cross-helicity. In other words, these two helicities are the only independent regular integral invariants of the coadjoint action of the MHD group $\textrm{SDiff}(M)\ltimes \mathfrak X^*(M)$, which is the semidirect product of the group of volume-preserving diffeomorphisms and the dual space of its Lie algebra.

    更新日期:2020-02-10
  • Density of g-Vector Cones From Triangulated Surfaces
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-09
    Yurikusa T.

    We study $g$-vector cones associated with clusters of cluster algebras defined from a marked surface $(S,M)$ of rank $n$. We determine the closure of the union of $g$-vector cones associated with all clusters. It is equal to $\mathbb{R}^n$ except for a closed surface with exactly one puncture, in which case it is equal to the half space of a certain explicit hyperplane in $\mathbb{R}^n$. Our main ingredients are laminations on $(S,M)$, their shear coordinates, and their asymptotic behavior under Dehn twists. As an application, if $(S,M)$ is not a closed surface with exactly one puncture, the exchange graph of cluster tilting objects in the corresponding cluster category is connected. If $(S,M)$ is a closed surface with exactly one puncture, it has precisely two connected components.

    更新日期:2020-02-10
  • A HYPERFINITE FACTOR WHICH IS NOT AN INJECTIVE C*-ALGEBRA
    Q. J. Math. (IF 0.636) Pub Date : 2020-02-05
    Wright J, Saitô K.

    We exhibit a wild monotone complete C*-algebra which is a hyperfinite factor but is not an injective C*-algebra.

    更新日期:2020-02-07
  • HOMOLOGICAL STABILITY FOR UNLINKED CIRCLES IN A 3-MANIFOLD
    Q. J. Math. (IF 0.636) Pub Date : 2020-02-05
    Kupers A.

    We prove a homological stability theorem for unlinked circles in $3$-manifolds and give an application to certain groups of diffeomorphisms of 3-manifolds.

    更新日期:2020-02-07
  • A SHARP ADAMS-TYPE INEQUALITY FOR WEIGHTED SOBOLEV SPACES
    Q. J. Math. (IF 0.636) Pub Date : 2020-02-07
    do Ó J, Macedo A, de Oliveira J.

    In a classical work (Ann. Math.128, (1988) 385–398), D. R. Adams proved a sharp Trudinger–Moser inequality for higher-order derivatives. We derive a sharp Adams-type inequality and Sobolev-type inequalities associated with a class of weighted Sobolev spaces that is related to a Hardy-type inequality.

    更新日期:2020-02-07
  • Chiral Versus Classical Operad
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-07
    Bakalov B, De Sole A, Heluani R, et al.

    We establish an explicit isomorphism between the associated graded of the filtered chiral operad and the classical operad, which is important for computing the cohomology of vertex algebras.

    更新日期:2020-02-07
  • Tractability properties of the discrepancy in Orlicz norms
    J. Complex. (IF 0.888) Pub Date : 2020-02-06
    Josef Dick; Aicke Hinrichs; Friedrich Pillichshammer; Joscha Prochno

    We show that the minimal discrepancy of a point set in the d-dimensional unit cube with respect to Orlicz norms can exhibit both polynomial and weak tractability. In particular, we show that the ψα-norms of exponential Orlicz spaces are polynomially tractable.

    更新日期:2020-02-07
  • Endofunctors and Poincaré–Birkhoff–Witt Theorems
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-06
    Dotsenko V, Tamaroff P.

    We determine what appears to be the bare-bones categorical framework for Poincaré–Birkhoff–Witt (PBW)-type theorems about universal enveloping algebras of various algebraic structures. Our language is that of endofunctors; we establish that a natural transformation of monads enjoys a PBW property only if that transformation makes its codomain a free right module over its domain. We conclude with a number of applications to show how this unified approach proves various old and new PBW-type theorems. In particular, we prove a PBW-type result for universal enveloping dendriform algebras of pre-Lie algebras, answering a question of Loday.

    更新日期:2020-02-07
  • Ordinary primes in Hilbert modular varieties
    Compos. Math. (IF 1.301) Pub Date : 2020-02-06
    Junecue Suh

    A well-known conjecture, often attributed to Serre, asserts that any motive over any number field has infinitely many ordinary reductions (in the sense that the Newton polygon coincides with the Hodge polygon). In the case of Hilbert modular cuspforms $f$ of parallel weight $(2,\ldots ,2)$ , we show how to produce more ordinary primes by using the Sato–Tate equidistribution and combining it with the Galois theory of the Hecke field. Under the assumption of stronger forms of Sato–Tate equidistribution, we get stronger (but conditional) results. In the case of higher weights, we formulate the ordinariness conjecture for submotives of the intersection cohomology of proper algebraic varieties with motivic coefficients, and verify it for the motives whose $\ell$ -adic Galois realisations are abelian on a finite-index subgroup. We get some results for Hilbert cuspforms of weight $(3,\ldots ,3)$ , weaker than those for $(2,\ldots ,2)$ .

    更新日期:2020-02-07
  • Weight enumerators, intersection enumerators, and Jacobi polynomials
    Discret. Math. (IF 0.728) Pub Date : 2020-02-05
    K. Honma; T. Okabe; M. Oura

    The intersection enumerator and the Jacobi polynomial in an arbitrary genus for a binary code are introduced. Adding the weight enumerator into our discussion, we give the explicit relations among them and give some of their basic properties.

    更新日期:2020-02-06
  • A note on estimates for elliptic systems with L1 data
    CR Math. (IF 0.611) Pub Date : 2019-11-27
    Bogdan Raita; Daniel Spector

    In this paper, we give necessary and sufficient conditions on the compatibility of a kth-order homogeneous linear elliptic differential operator A and differential constraint C for solutions toAu=fsubject toCf=0 in Rn to satisfy the estimates‖Dk−ju‖Lnn−j(Rn)⩽c‖f‖L1(Rn) for j∈{1,…,min⁡{k,n−1}} and‖Dk−nu‖L∞(Rn)⩽c‖f‖L1(Rn) when k≥n.

    更新日期:2020-02-06
  • Continuity of a surface in Fréchet spaces
    CR Math. (IF 0.611) Pub Date : 2019-11-06
    Philippe G. Ciarlet; Maria Malin; Cristinel Mardare

    We establish the continuity of a surface as a function of its first two fundamental forms for several Fréchet topologies, which include in particular those of the space Wloc1,p for the first fundamental form and of the space Llocp for the second fundamental form, for any p>2.

    更新日期:2020-02-06
  • Linear response for random dynamical systems
    Adv. Math. (IF 1.435) Pub Date : 2020-02-05
    Wael Bahsoun; Marks Ruziboev; Benoît Saussol

    We study for the first time linear response for random compositions of maps, chosen independently according to a distribution P. We are interested in the following question: how does an absolutely continuous stationary measure (acsm) of a random system change when P changes smoothly to Pε? For a wide class of one dimensional random maps, we prove differentiability of acsm with respect to ε; moreover, we obtain a linear response formula. Our results cover random maps whose transfer operator does not necessarily admit a spectral gap. We apply our results to iid compositions, with respect to various distributions Pε, of uniformly expanding circle maps, Gauss-Rényi maps (random continued fractions) and Pomeau-Manneville maps. Our results yield an exact formula for the invariant density of random continued fractions; while for Pomeau-Manneville maps our results provide a precise relation between their linear response under certain random perturbations and their linear response under deterministic perturbations.

    更新日期:2020-02-06
  • A Sharp Lorentz-Invariant Strichartz Norm Expansion for the Cubic Wave Equation in ℝ1+3
    Q. J. Math. (IF 0.636) Pub Date : 2020-02-03
    Negro G.

    We provide an asymptotic formula for the maximal Strichartz norm of small solutions to the cubic wave equation in Minkowski space. The leading coefficient is given by Foschi’s sharp constant for the linear Strichartz estimate. We calculate the constant in the second term, which differs depending on whether the equation is focussing or defocussing. The sign of this coefficient also changes accordingly.

    更新日期:2020-02-06
  • ON TANGENCY IN EQUISINGULAR FAMILIES OF CURVES AND SURFACES
    Q. J. Math. (IF 0.636) Pub Date : 2020-02-03
    Giles Flores A, Silva O, Snoussi J.

    We study the behavior of limits of tangents in topologically equivalent spaces. In the context of families of generically reduced curves, we introduce the $s$-invariant of a curve and we show that in a Whitney equisingular family with the property that the $s$-invariant is constant along the parameter space, the number of tangents of each curve of the family is constant. In the context of families of isolated surface singularities, we show through examples that Whitney equisingularity is not sufficient to ensure that the tangent cones of the family are homeomorphic. We explain how the existence of exceptional tangents is preserved by Whitney equisingularity but their number can change.

    更新日期:2020-02-06
  • ON RELATIVE COMPLETE REDUCIBILITY
    Q. J. Math. (IF 0.636) Pub Date : 2020-02-05
    Attenborough C, Bate M, Gruchot M, et al.

    Let $K$ be a reductive subgroup of a reductive group $G$ over an algebraically closed field $k$. The notion of relative complete reducibility, introduced in [M. Bate, B. Martin, G. Röhrle, R. Tange, Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras, Math. Z.269 (2011), no. 1, 809–832], gives a purely algebraic description of the closed $K$-orbits in $G^n$, where $K$ acts by simultaneous conjugation on $n$-tuples of elements from $G$. This extends work of Richardson and is also a natural generalization of Serre’s notion of $G$-complete reducibility. In this paper we revisit this idea, giving a characterization of relative $G$-complete reducibility, which directly generalizes equivalent formulations of $G$-complete reducibility. If the ambient group $G$ is a general linear group, this characterization yields representation-theoretic criteria. Along the way, we extend and generalize several results from [M. Bate, B. Martin, G. Röhrle, R. Tange, Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras, Math. Z.269 (2011), no. 1, 809–832].

    更新日期:2020-02-06
  • Existence and Density of General Components of the Noether–Lefschetz Locus on Normal Threefolds
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-05
    Bruzzo U, Grassi A, Lopez A.

    We consider the Noether–Lefschetz problem for surfaces in ${\mathbb Q}$-factorial normal 3-folds with rational singularities. We show the existence of components of the Noether–Lefschetz locus of maximal codimension, and that there are indeed infinitely many of them. Moreover, we show that their union is dense in the natural topology.

    更新日期:2020-02-06
  • On the $K(\unicode[STIX]{x1D70B},1)$ -problem for restrictions of complex reflection arrangements
    Compos. Math. (IF 1.301) Pub Date : 2020-01-20
    Nils Amend; Pierre Deligne; Gerhard Röhrle

    Let $W\subset \operatorname{GL}(V)$ be a complex reflection group and $\mathscr{A}(W)$ the set of the mirrors of the complex reflections in  $W$ . It is known that the complement $X(\mathscr{A}(W))$ of the reflection arrangement $\mathscr{A}(W)$ is a $K(\unicode[STIX]{x1D70B},1)$ space. For $Y$ an intersection of hyperplanes in $\mathscr{A}(W)$ , let $X(\mathscr{A}(W)^{Y})$ be the complement in $Y$ of the hyperplanes in $\mathscr{A}(W)$ not containing  $Y$ . We hope that $X(\mathscr{A}(W)^{Y})$ is always a $K(\unicode[STIX]{x1D70B},1)$ . We prove it in case of the monomial groups $W=G(r,p,\ell )$ . Using known results, we then show that there remain only three irreducible complex reflection groups, leading to just eight such induced arrangements for which this $K(\unicode[STIX]{x1D70B},1)$ property remains to be proved.

    更新日期:2020-02-06
  • ON THE ASSOCIATED PRIMES OF LOCAL COHOMOLOGY
    Nagoya Math. J. (IF 0.638) Pub Date : 2018-02-05
    HAILONG DAO; PHAM HUNG QUY

    Let $R$ be a commutative Noetherian ring of prime characteristic $p$ . In this paper, we give a short proof using filter regular sequences that the set of associated prime ideals of $H_{I}^{t}(R)$ is finite for any ideal $I$ and for any $t\geqslant 0$ when $R$ has finite $F$ -representation type or finite singular locus. This extends a previous result by Takagi–Takahashi and gives affirmative answers for a problem of Huneke in many new classes of rings in positive characteristic. We also give a criterion about the singularities of $R$ (in any characteristic) to guarantee that the set $\operatorname{Ass}H_{I}^{2}(R)$ is always finite.

    更新日期:2020-02-06
  • STRONGLY QUASI-HEREDITARY ALGEBRAS AND REJECTIVE SUBCATEGORIES
    Nagoya Math. J. (IF 0.638) Pub Date : 2018-02-27
    MAYU TSUKAMOTO

    Ringel’s right-strongly quasi-hereditary algebras are a distinguished class of quasi-hereditary algebras of Cline–Parshall–Scott. We give characterizations of these algebras in terms of heredity chains and right rejective subcategories. We prove that any artin algebra of global dimension at most two is right-strongly quasi-hereditary. Moreover we show that the Auslander algebra of a representation-finite algebra $A$ is strongly quasi-hereditary if and only if $A$ is a Nakayama algebra.

    更新日期:2020-02-06
  • LITTLEWOOD–PALEY CHARACTERIZATIONS OF ANISOTROPIC WEAK MUSIELAK–ORLICZ HARDY SPACES
    Nagoya Math. J. (IF 0.638) Pub Date : 2018-03-16
    BO LI; RUIRUI SUN; MINFENG LIAO; BAODE LI

    Let $A$ be an expansive dilation on $\mathbb{R}^{n}$ and $\unicode[STIX]{x1D711}:\mathbb{R}^{n}\times [0,\infty )\rightarrow [0,\infty )$ an anisotropic growth function. In this article, the authors introduce the anisotropic weak Musielak–Orlicz Hardy space $\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$ via the nontangential grand maximal function and then obtain its Littlewood–Paley characterizations in terms of the anisotropic Lusin-area function, $g$ -function or $g_{\unicode[STIX]{x1D706}}^{\ast }$ -function, respectively. All these characterizations for anisotropic weak Hardy spaces $\mathit{WH}_{A}^{p}(\mathbb{R}^{n})$ (namely, $\unicode[STIX]{x1D711}(x,t):=t^{p}$ for all $t\in [0,\infty )$ and $x\in \mathbb{R}^{n}$ with $p\in (0,1]$ ) are new. Moreover, the range of $\unicode[STIX]{x1D706}$ in the anisotropic $g_{\unicode[STIX]{x1D706}}^{\ast }$ -function characterization of $\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$ coincides with the best known range of the $g_{\unicode[STIX]{x1D706}}^{\ast }$ -function characterization of classical Hardy space $H^{p}(\mathbb{R}^{n})$ or its weighted variants, where $p\in (0,1]$ .

    更新日期:2020-02-06
  • FRACTIONAL FOCK–SOBOLEV SPACES
    Nagoya Math. J. (IF 0.638) Pub Date : 2018-03-06
    HONG RAE CHO; SOOHYUN PARK

    Let $s\in \mathbb{R}$ and $0

    更新日期:2020-02-06
  • MULTIPLICATION FORMULAS AND SEMISIMPLICITY FOR $q$ -SCHUR SUPERALGEBRAS
    Nagoya Math. J. (IF 0.638) Pub Date : 2018-04-30
    JIE DU; HAIXIA GU; ZHONGGUO ZHOU

    We investigate products of certain double cosets for the symmetric group and use the findings to derive some multiplication formulas for the $q$ -Schur superalgebras. This gives a combinatorialization of the relative norm approach developed in Du and Gu (A realization of the quantum supergroup $\mathbf{U}(\mathfrak{g}\mathfrak{l}_{m|n})$ , J. Algebra 404 (2014), 60–99). We then give several applications of the multiplication formulas, including the matrix representation of the regular representation and a semisimplicity criterion for $q$ -Schur superalgebras. We also construct infinitesimal and little $q$ -Schur superalgebras directly from the multiplication formulas and develop their semisimplicity criteria.

    更新日期:2020-02-06
  • RANKIN–SELBERG CONVOLUTIONS OF NONCUSPIDAL HALF-INTEGRAL WEIGHT MAASS FORMS IN THE PLUS SPACE
    Nagoya Math. J. (IF 0.638) Pub Date : 2018-05-21
    YOSHINORI MIZUNO

    The author gives the analytic properties of the Rankin–Selberg convolutions of two half-integral weight Maass forms in the plus space. Applications to the Koecher–Maass series associated with nonholomorphic Siegel–Eisenstein series are given.

    更新日期:2020-02-06
  • DISTRIBUTION OF GALOIS GROUPS OF MAXIMAL UNRAMIFIED 2-EXTENSIONS OVER IMAGINARY QUADRATIC FIELDS
    Nagoya Math. J. (IF 0.638) Pub Date : 2018-07-09
    SOSUKE SASAKI

    Let $k$ be an imaginary quadratic field with $\operatorname{Cl}_{2}(k)\simeq V_{4}$ . It is known that the length of the Hilbert $2$ -class field tower is at least $2$ . Gerth (On 2-class field towers for quadratic number fields with $2$ -class group of type $(2,2)$ , Glasgow Math. J. 40(1) (1998), 63–69) calculated the density of $k$ where the length of the tower is $1$ ; that is, the maximal unramified $2$ -extension is a $V_{4}$ -extension. In this paper, we shall extend this result for generalized quaternion, dihedral, and semidihedral extensions of small degrees.

    更新日期:2020-02-06
  • GORENSTEIN HOMOLOGICAL PROPERTIES OF TENSOR RINGS
    Nagoya Math. J. (IF 0.638) Pub Date : 2018-06-07
    XIAO-WU CHEN; MING LU

    Let $R$ be a two-sided Noetherian ring, and let $M$ be a nilpotent $R$ -bimodule, which is finitely generated on both sides. We study Gorenstein homological properties of the tensor ring $T_{R}(M)$ . Under certain conditions, the ring $R$ is Gorenstein if and only if so is $T_{R}(M)$ . We characterize Gorenstein projective $T_{R}(M)$ -modules in terms of $R$ -modules.

    更新日期:2020-02-06
  • NMJ volume 237 Cover and Front matter
    Nagoya Math. J. (IF 0.638) Pub Date : 2020-02-05

    None

    更新日期:2020-02-06
  • NMJ volume 237 Cover and Back matter
    Nagoya Math. J. (IF 0.638) Pub Date : 2020-02-05

    None

    更新日期:2020-02-06
  • The Orlicz Aleksandrov Problem for Orlicz Integral Curvature
    Int. Math. Res. Notices (IF 1.452) Pub Date : 2020-02-04
    Feng Y, He B.

    In this paper, the Orlicz integral curvature is introduced, and some of its basic properties are discussed. The Orlicz Aleksandrov problem characterizing the Orlicz integral curvature is posed. The problem is solved in two situations when the given measure is even.

    更新日期:2020-02-04
  • A BETTER COMPARISON OF $\operatorname{cdh}$ - AND $l\operatorname{dh}$ -COHOMOLOGIES
    Nagoya Math. J. (IF 0.638) Pub Date : 2019-09-13
    SHANE KELLY

    In order to work with non-Nagata rings which are Nagata “up-to-completely-decomposed-universal-homeomorphism,” specifically finite rank Hensel valuation rings, we introduce the notions of pseudo-integral closure, pseudo-normalization, and pseudo-Hensel valuation ring. We use this notion to give a shorter and more direct proof that $H_{\operatorname{cdh}}^{n}(X,F_{\operatorname{cdh}})=H_{l\operatorname{dh}}^{n}(X,F_{l\operatorname{dh}})$ for homotopy sheaves $F$ of modules over the $\mathbb{Z}_{(l)}$ -linear motivic Eilenberg–Maclane spectrum. This comparison is an alternative to the first half of the author’s volume Astérisque 391 whose main theorem is a cdh-descent result for Voevodsky motives. The motivating new insight is really accepting that Voevodsky’s motivic cohomology (with $\mathbb{Z}[\frac{1}{p}]$ -coefficients) is invariant not just for nilpotent thickenings, but for all universal homeomorphisms.

    更新日期:2020-02-04
  • Bipartite complements of circle graphs
    Discret. Math. (IF 0.728) Pub Date : 2020-02-01
    Louis Esperet; Matěj Stehlík

    Using an algebraic characterization of circle graphs, Bouchet proved in 1999 that if a bipartite graph G is the complement of a circle graph, then G is a circle graph. We give an elementary proof of this result.

    更新日期:2020-02-03
  • A generalization of Noel–Reed–Wu Theorem to signed graphs
    Discret. Math. (IF 0.728) Pub Date : 2020-02-01
    Wei Wang; Jianguo Qian

    Let Σ be a signed graph where two edges joining the same pair of vertices with opposite signs are allowed. The zero-free chromatic number χ∗(Σ) of Σ is the minimum even integer 2k such that G admits a proper coloring f:V(Σ)↦{±1,±2,…,±k}. The zero-free list chromatic number χl∗(Σ) is the list version of zero-free chromatic number. Σ is called zero-free chromatic-choosable if χl∗(Σ)=χ∗(Σ). We show that if Σ has at most χ∗(Σ)+1 vertices then Σ is zero-free chromatic-choosable. This result strengthens Noel–Reed–Wu Theorem which states that every graph G with at most 2χ(G)+1 vertices is chromatic-choosable, where χ(G) is the chromatic number of G.

    更新日期:2020-02-03
  • Equivariant localization and completion in cyclic homology and derived loop spaces
    Adv. Math. (IF 1.435) Pub Date : 2020-02-03
    Harrison Chen

    We prove an equivariant localization theorem over an algebraically closed field of characteristic zero for smooth quotient stacks by reductive groups X/G in the setting of derived loop spaces as well as Hochschild homology and its cyclic variants. We show that the derived loop spaces of the stack X/G and its classical z-fixed point stack π0(Xz)/Gz become equivalent after completion along a semisimple parameter [z]∈G//G, implying the analogous statement for Hochschild and cyclic homology of the dg category of perfect complexes Perf(X/G). We then prove an analogue of the Atiyah-Segal completion theorem in the setting of periodic cyclic homology, where the completion of the periodic cyclic homology of Perf(X/G) at the identity [e]∈G//G is identified with a 2-periodic version of the derived de Rham cohomology of X/G. Together, these results identify the completed periodic cyclic homology of a stack X/G over a parameter [z]∈G//G with the 2-periodic derived de Rham cohomology of its z-fixed points.

    更新日期:2020-02-03
  • Vector Lattices Admitting a Positively Homogeneous Continuous Function Calculus
    Q. J. Math. (IF 0.636) Pub Date : 2020-01-25
    Laustsen N, Troitsky V.

    We characterize the Archimedean vector lattices that admit a positively homogeneous continuous function calculus by showing that the following two conditions are equivalent for each $n$-tuple $\boldsymbol{x} = (x_1,\ldots ,x_n)\in X^n$, where $X$ is an Archimedean vector lattice and $n\in{\mathbb{N}}$: • there is a vector lattice homomorphism $\Phi _{\boldsymbol{x}}\colon H_n\to X$ such that $$\begin{equation*}\Phi_{\boldsymbol{x}}(\pi_i^{(n)}) = x_i\qquad (i\in\{1,\ldots,n\}),\end{equation*}$$where $H_n$ denotes the vector lattice of positively homogeneous, continuous, real-valued functions defined on ${\mathbb{R}}^n$ and $\pi _i^{(n)}\colon{\mathbb{R}}^n\to{\mathbb{R}}$ is the $i^{\text{}}$th coordinate projection; • there is a positive element $e\in X$ such that $e\geqslant \lvert x_1\rvert \vee \cdots \vee \lvert x_n\rvert$ and the norm$$\begin{equation*}\lVert x\rVert_e = \inf\bigl\{ \lambda\in[0,\infty)\:\colon\:\lvert x\rvert{\leqslant}\lambda e\bigr\},\end{equation*}$$defined for each $x$ in the order ideal $I_e$ of $X$ generated by $e$, is complete when restricted to the closed sublattice of $I_e$ generated by $x_1,\ldots ,x_n$.Moreover, we show that a vector space which admits a ‘sufficiently strong’ $H_n$-function calculus for each $n\in{\mathbb{N}}$ is automatically a vector lattice, and we explore the situation in the non-Archimedean case by showing that some non-Archimedean vector lattices admit a positively homogeneous continuous function calculus, while others do not.

    更新日期:2020-02-03
  • WARING’S PROBLEM FOR RATIONAL FUNCTIONS IN ONE VARIABLE
    Q. J. Math. (IF 0.636) Pub Date : 2020-02-03
    Im B, Larsen M.

    Let $f\in{\mathbb{Q}}(x)$ be a non-constant rational function. We consider ‘Waring’s problem for $f(x)$,’ i.e., whether every element of ${\mathbb{Q}}$ can be written as a bounded sum of elements of $\{f(a)\mid a\in{\mathbb{Q}}\}$. For rational functions of degree $2$, we give necessary and sufficient conditions. For higher degrees, we prove that every polynomial of odd degree and every odd Laurent polynomial satisfies Waring’s problem. We also consider the ‘easier Waring’s problem’: whether every element of ${\mathbb{Q}}$ can be represented as a bounded sum of elements of $\{\pm f(a)\mid a\in{\mathbb{Q}}\}$.

    更新日期:2020-02-03
Contents have been reproduced by permission of the publishers.
导出
全部期刊列表>>
化学/材料学中国作者研究精选
Springer Nature 2019高下载量文章和章节
ACS材料视界
南京大学
自然科研论文编辑服务
剑桥大学-
中国科学院大学化学科学学院
南开大学化学院周其林
课题组网站
X-MOL
北京大学分子工程苏南研究院
华东师范大学分子机器及功能材料
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug