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  • Transferring spherical multipliers on compact symmetric spaces
    Math. Z. (IF 0.881) Pub Date : 2021-01-21
    Sanjiv Kumar Gupta, Kathryn E. Hare

    We prove a two-sided transference theorem between \(L^{p}\) spherical multipliers on the compact symmetric space U/K and \(L^{p}\) multipliers on the vector space \(i{\mathfrak {p}},\) where the Lie algebra of U has Cartan decomposition \(\mathfrak {k\oplus }i{\mathfrak {p}}\). This generalizes the classic theorem transference theorem of deLeeuw relating multipliers on \( L^{p}(\mathbb {T)}\) and \(L^{p}(\mathbb

    更新日期:2021-01-21
  • Grothendieck–Lefschetz for ample subvarieties
    Math. Z. (IF 0.881) Pub Date : 2021-01-18
    Tommaso de Fernex, Chung Ching Lau

    We establish a Grothendieck–Lefschetz theorem for smooth ample subvarieties of smooth projective varieties over an algebraically closed field of characteristic zero and, more generally, for smooth subvarieties whose complement has small cohomological dimension. A weaker statement is also proved in a more general context and in all characteristics. Several applications are included.

    更新日期:2021-01-18
  • On norm almost periodic measures
    Math. Z. (IF 0.881) Pub Date : 2021-01-16
    Timo Spindeler, Nicolae Strungaru

    In this paper, we study norm almost periodic measures on locally compact Abelian groups. First, we show that the norm almost periodicity of \(\mu \) is equivalent to the equi-Bohr almost periodicity of \(\mu *g\) for all g in a fixed family of functions. Then, we show that, for absolutely continuous measures, norm almost periodicity is equivalent to the Stepanov almost periodicity of the Radon–Nikodym

    更新日期:2021-01-18
  • Symmetric shift-invariant subspaces and harmonic maps
    Math. Z. (IF 0.881) Pub Date : 2021-01-12
    Alexandru Aleman, Rui Pacheco, John C. Wood

    The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class of harmonic maps into symmetric and k-symmetric spaces. Using an appropriate description of such symmetric shift-invariant subspaces we obtain new

    更新日期:2021-01-13
  • On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four
    Math. Z. (IF 0.881) Pub Date : 2021-01-12
    Lie Fu, Grégoire Menet

    We extend a result of Guan by showing that the second Betti number of a 4-dimensional primitively symplectic orbifold is at most 23 and there are at most 91 singular points. The maximal possibility 23 can only occur in the smooth case. In addition to the known smooth examples with second Betti numbers 7 and 23, we provide examples of such orbifolds with second Betti numbers 3, 5, 6, 8, 9, 10, 11, 14

    更新日期:2021-01-13
  • 2-Verma modules and the Khovanov–Rozansky link homologies
    Math. Z. (IF 0.881) Pub Date : 2021-01-12
    Grégoire Naisse, Pedro Vaz

    We explain how Queffelec–Sartori’s construction of the HOMFLY-PT link polynomial can be interpreted in terms of parabolic Verma modules for \({\mathfrak {gl}_{2n}}\). Lifting the construction to the world of categorification, we use parabolic 2-Verma modules to give a higher representation theory construction of Khovanov–Rozansky’s triply graded link homology.

    更新日期:2021-01-12
  • Segre nondegenerate totally real subvarieties
    Math. Z. (IF 0.881) Pub Date : 2021-01-12
    Bernhard Lamel, Jiří Lebl

    We study an irreducible real-analytic germ of an n-dimensional variety in n dimensional complex space. Assuming that the variety is Segre nondegenerate we define an averaging operator that generalizes the Moser–Webster involution. This operator can be thought of as being the CR structure of the singularity, and using this operator we study the set of functions that are restrictions of holomorphic functions

    更新日期:2021-01-12
  • Quasi-cyclic modules and coregular sequences
    Math. Z. (IF 0.881) Pub Date : 2021-01-09
    Robin Hartshorne, Claudia Polini

    We develop the theory of coregular sequences and codepth for modules that need not be finitely generated or artinian over a Noetherian ring. We use this theory to give a new version of a theorem of Hellus characterizing set-theoretic complete intersections in terms of local cohomology modules. We also define quasi-cyclic modules as increasing unions of cyclic modules, and show that modules of codepth

    更新日期:2021-01-10
  • On scales of Sobolev spaces associated to generalized Hardy operators
    Math. Z. (IF 0.881) Pub Date : 2021-01-09
    Konstantin Merz

    We consider the fractional Laplacian with Hardy potential and compare the scale of homogeneous \(L^p\) Sobolev spaces generated by this operator with the ordinary homogeneous Sobolev spaces. The proof relies on a generalized Hardy inequality, a reversed Hardy inequality expressed in terms of square functions, and a Hörmander multiplier theorem which is proven for positive coupling constants. The latter

    更新日期:2021-01-10
  • Exponential sums over cubes of primes in short intervals and its applications
    Math. Z. (IF 0.881) Pub Date : 2021-01-09
    Taiyu Li, Yanjun Yao

    In this paper, we treat the estimate on exponential sums over cubes of primes in short intervals, and improve a previous bound of Kumchev (in: Number Theory: Arithmetic in Shangri-La (Proc. China-Japan Seminar Number Theory), pp. 116–131, World Scientific, Singapore, 2013). Moreover, we present some applications to the cubic Waring–Goldbach problem.

    更新日期:2021-01-10
  • Grothendieck groups, convex cones and maximal Cohen–Macaulay points
    Math. Z. (IF 0.881) Pub Date : 2021-01-08
    Ryo Takahashi

    Let R be a commutative noetherian ring. Let \(\mathsf {H}(R)\) be the quotient of the Grothendieck group of finitely generated R-modules by the subgroup generated by pseudo-zero modules. Suppose that the \(\mathbb {R}\)-vector space \(\mathsf {H}(R)_\mathbb {R}=\mathsf {H}(R)\otimes _\mathbb {Z}\mathbb {R}\) has finite dimension. Let \(\mathsf {C}(R)\) (resp. \(\mathsf {C}_r(R)\)) be the convex cone

    更新日期:2021-01-10
  • On $$\mathrm {G}_2$$ G 2 and sub-Riemannian model spaces of step and rank three
    Math. Z. (IF 0.881) Pub Date : 2021-01-08
    Eirik Berge, Erlend Grong

    We give the complete classification of all sub-Riemannian model spaces with both step and rank three. Model spaces in this context refer to spaces where any infinitesimal isometry between horizontal tangent spaces can be integrated to a full isometry. They will be divided into three families based on their nilpotentization. Each family will depend on a different number of parameters, making the result

    更新日期:2021-01-10
  • Covers and direct limits: a contramodule-based approach
    Math. Z. (IF 0.881) Pub Date : 2021-01-08
    Silvana Bazzoni, Leonid Positselski

    We present applications of contramodule techniques to the Enochs conjecture about covers and direct limits, both in the categorical tilting context and beyond. In the n-tilting–cotilting correspondence situation, if \(\mathsf A\) is a Grothendieck abelian category and the related abelian category \(\mathsf B\) is equivalent to the category of contramodules over a topological ring \(\mathfrak R\) belonging

    更新日期:2021-01-08
  • Functional relations for solutions of q -difference equations
    Math. Z. (IF 0.881) Pub Date : 2021-01-07
    Thomas Dreyfus, Charlotte Hardouin, Julien Roques

    In this paper, we study the algebraic relations satisfied by the solutions of q-difference equations and their transforms with respect to an auxiliary operator. Our main tools are the parametrized Galois theories developed in Hardouin and Singer (Math Ann 342(2):333–377, 2008) and Ovchinnikov and Wibmer (Int Math Res Not 12:3962–4018, 2015). The first part of this paper is concerned with the case where

    更新日期:2021-01-08
  • Inequality conjectures on derivations of local k -th Hessain algebras associated to isolated hypersurface singularities
    Math. Z. (IF 0.881) Pub Date : 2021-01-07
    Naveed Hussain, Stephen S.-T. Yau, Huaiqing Zuo

    Let (V, 0) be an isolated hypersurface singularity. We introduce a series of new derivation Lie algebras \(L_{k}(V)\) associated to (V, 0). Its dimension is denoted as \(\lambda _{k}(V)\). The \(L_{k}(V)\) is a generalization of the Yau algebra L(V) and \(L_{0}(V)=L(V)\). These numbers \(\lambda _{k}(V)\) are new numerical analytic invariants of an isolated hypersurface singularity. In this article

    更新日期:2021-01-08
  • Surgery for partially hyperbolic dynamical systems II. Blow-up of a complex curve
    Math. Z. (IF 0.881) Pub Date : 2021-01-07
    Andrey Gogolev, Federico Rodriguez Hertz

    In this paper we use the blow-up surgery introduced in [1] to produce new higher dimensional partially hyperbolic flows. The main contribution of the paper is the slow-down construction which accompanies the blow-up construction. This new ingredient allows to dispose of a rather strong domination assumption which was crucial for results in [1]. Consequently we gain more flexibility which allows to

    更新日期:2021-01-08
  • Explicit counterexamples to the weak Muckenhoupt–Wheeden conjecture
    Math. Z. (IF 0.881) Pub Date : 2021-01-07
    Adam Osękowski

    We present an explicit construction of examples showing that the estimate \(\Vert T^\epsilon \Vert _{L^1(w)\rightarrow L^{1,\infty }(w)}\)\(\lesssim [w]_{A_1}\log (1+[w]_{A_1})\) for Haar multipliers is sharp in terms of the characteristic \([w]_{A_1}\).

    更新日期:2021-01-08
  • Elliptic characterization and unification of Oka maps
    Math. Z. (IF 0.881) Pub Date : 2021-01-07
    Yuta Kusakabe

    We generalize our elliptic characterization of Oka manifolds to Oka maps. The generalized characterization can be considered as an affirmative answer to the relative version of Gromov’s conjecture. As an application, we unify previously known Oka principles for submersions; namely the Gromov type Oka principle for subelliptic submersions and the Forstnerič type Oka principle for holomorphic fiber bundles

    更新日期:2021-01-07
  • Hilbert series in the category of trees with contractions
    Math. Z. (IF 0.881) Pub Date : 2021-01-07
    Eric Ramos

    We consider Hilbert series associated to modules over various categories of trees. Using the technology of Sam and Snowden (J Am Math Soc 30(1): 159–203, 2017) we show that these Hilbert series must be algebraic. We then apply these technical theorems to prove facts about certain natural generating functions associated to trees.

    更新日期:2021-01-07
  • Brauer class over the Picard scheme of totally degenerate stable curves
    Math. Z. (IF 0.881) Pub Date : 2021-01-06
    Qixiao Ma

    We study the Brauer class rising from the obstruction to the existence of tautological line bundles on the Picard scheme of curves. We determine the period and index of that Brauer class in certain cases.

    更新日期:2021-01-07
  • Equivariant Iwasawa theory for elliptic curves
    Math. Z. (IF 0.881) Pub Date : 2021-01-06
    Takenori Kataoka

    We discuss abelian equivariant Iwasawa theory for elliptic curves over \({\mathbb {Q}}\) at good supersingular primes and non-anomalous good ordinary primes. Using Kobayashi’s method, we construct equivariant Coleman maps, which send the Beilinson–Kato element to the equivariant p-adic L-functions. Then we propose equivariant main conjectures and, under certain assumptions, prove one divisibility via

    更新日期:2021-01-06
  • Poincaré-Sobolev inequalities with rearrangement-invariant norms on the entire space
    Math. Z. (IF 0.881) Pub Date : 2021-01-06
    Zdeněk Mihula

    Poincaré-Sobolev-type inequalities involving rearrangement-invariant norms on the entire \(\mathbb R^n\) are provided. Namely, inequalities of the type \(\Vert u-P\Vert _{Y(\mathbb R^n)}\le C\Vert \nabla ^m u\Vert _{X(\mathbb R^n)}\), where X and Y are either rearrangement-invariant spaces over \(\mathbb R^n\) or Orlicz spaces over \(\mathbb R^n\), u is a \(m-\)times weakly differentiable function

    更新日期:2021-01-06
  • Representations with minimal support for quantized Gieseker varieties
    Math. Z. (IF 0.881) Pub Date : 2021-01-06
    Pavel Etingof, Vasily Krylov, Ivan Losev, José Simental

    We study the minimally supported representations of quantizations of Gieseker moduli spaces. We relate them to \({\text {SL}}_n\)-equivariant D-modules on the nilpotent cone of \(\mathfrak {sl}_n\) and to minimally supported representations of type A rational Cherednik algebras. Our main result is character formulas for minimally supported representations of quantized Gieseker moduli spaces.

    更新日期:2021-01-06
  • A lower bound for the number of odd-degree representations of a finite group
    Math. Z. (IF 0.881) Pub Date : 2021-01-05
    Nguyen Ngoc Hung, Thomas Michael Keller, Yong Yang

    Let G be a finite group and P a Sylow 2-subgroup of G. We obtain both asymptotic and explicit bounds for the number of odd-degree irreducible complex representations of G in terms of the size of the abelianization of P. To do so, we, on one hand, make use of the recent proof of the McKay conjecture for the prime 2 by Malle and Späth, and, on the other hand, prove lower bounds for the class number of

    更新日期:2021-01-06
  • $$L^2$$ L 2 boundedness of Hilbert transforms along variable flat curves
    Math. Z. (IF 0.881) Pub Date : 2021-01-05
    Junfeng Li, Haixia Yu

    In this paper, the \(L^2\) boundedness of the Hilbert transform along variable flat curve \((t,P(x_1)\gamma (t))\)$$\begin{aligned} H_{P,\gamma }f(x_1,x_2):=\mathrm {p.\,v.}\int _{-\infty }^{\infty }f(x_1-t,x_2-P(x_1)\gamma (t))\,\frac{\text {d}t}{t},\quad \forall \, (x_1,x_2)\in {\mathbb {R}}^2, \end{aligned}$$ is studied, where P is a real polynomial on \({\mathbb {R}}\). A new sufficient condition

    更新日期:2021-01-05
  • Maximal operators on Lorentz spaces in non-doubling setting
    Math. Z. (IF 0.881) Pub Date : 2021-01-04
    Dariusz Kosz

    We study mapping properties of the centered Hardy–Littlewood maximal operator \(\mathcal {M}\) acting on Lorentz spaces \(L^{p,q}({\mathfrak {X}})\) in the context of certain non-doubling metric measure spaces \({\mathfrak {X}}\). The special class of spaces for which these properties are very peculiar is introduced and many examples are given. In particular, for each \(p_0, q_0, r_0 \in (1, \infty

    更新日期:2021-01-05
  • Atypical points at infinity and algorithmic detection of the bifurcation locus of real polynomials
    Math. Z. (IF 0.881) Pub Date : 2021-01-04
    Luis Renato G. Dias, Cezar Joiţa, Mihai Tibăr

    We show that the variation of the topology at infinity of a two-variable polynomial function is localisable at a finite number of “atypical points” at infinity. We construct an effective algorithm with low complexity in order to detect sharply the bifurcation values of the polynomial function.

    更新日期:2021-01-04
  • Regularity and Koszul property of symbolic powers of monomial ideals
    Math. Z. (IF 0.881) Pub Date : 2021-01-02
    Le Xuan Dung, Truong Thi Hien, Hop D. Nguyen, Tran Nam Trung

    Let I be a homogeneous ideal in a polynomial ring over a field. Let \(I^{(n)}\) be the n-th symbolic power of I. Motivated by results about ordinary powers of I, we study the asymptotic behavior of the regularity function \({{\,\mathrm{reg}\,}}(I^{(n)})\) and the maximal generating degree function \(\omega (I^{(n)})\), when I is a monomial ideal. It is known that both functions are eventually quasi-linear

    更新日期:2021-01-03
  • A quantum cluster algebra approach to representations of simply laced quantum affine algebras
    Math. Z. (IF 0.881) Pub Date : 2020-12-23
    Léa Bittmann

    We establish a quantum cluster algebra structure on the quantum Grothendieck ring of a certain monoidal subcategory of the category of finite-dimensional representations of a simply-laced quantum affine algebra. Moreover, the (q, t)-characters of certain irreducible representations, among which fundamental representations, are obtained as quantum cluster variables. This approach gives a new algorithm

    更新日期:2020-12-23
  • The spectral decomposition of $$|\theta |^2$$ | θ | 2
    Math. Z. (IF 0.881) Pub Date : 2020-12-17
    Paul D. Nelson

    Let \(\theta \) be an elementary theta function, such as the classical Jacobi theta function. We establish a spectral decomposition and surprisingly strong asymptotic formulas for \(\langle |\theta |^2, \varphi \rangle \) as \(\varphi \) traverses a sequence of Hecke-translates of a nice enough fixed function. The subtlety is that typically \(|\theta |^2 \notin L^2\). Applications to the subconvexity

    更新日期:2020-12-17
  • Correction to: Einstein four-manifolds of three-nonnegative curvature operator
    Math. Z. (IF 0.881) Pub Date : 2020-12-16
    Peng Wu

    This is to acknowledge that the main results of the article [3] were first proved in a joint preprint with Xiaodong Cao [1].

    更新日期:2020-12-16
  • On geometric quantization of $$b^m$$ b m -symplectic manifolds
    Math. Z. (IF 0.881) Pub Date : 2020-08-25
    Victor W. Guillemin, Eva Miranda, Jonathan Weitsman

    We study the formal geometric quantization of \(b^m\)-symplectic manifolds equipped with Hamiltonian actions of a torus T with nonzero leading modular weight. The resulting virtual \(T-\)modules are finite dimensional when m is odd, as in [4]; when m is even, these virtual modules are not finite dimensional, and we compute the asymptotics of the representations for large weight.

    更新日期:2020-08-25
  • Teichmüller spaces and Torelli theorems for hyperkähler manifolds
    Math. Z. (IF 0.881) Pub Date : 2020-08-20
    Eduard Looijenga

    Kreck and Yang Su recently gave counterexamples to a version of the Torelli theorem for hyperkählerian manifolds as stated by Verbitsky. We extract the correct statement and give a short proof of it. We also revisit a few of its consequences, some of which are given new (shorter) proofs, and ask some questions.

    更新日期:2020-08-20
  • Energy distribution of harmonic 1-forms and Jacobians of Riemann surfaces with a short closed geodesic
    Math. Z. (IF 0.881) Pub Date : 2020-08-17
    Peter Buser, Eran Makover, Bjoern Muetzel, Robert Silhol

    We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian variety of S develops into a variety that splits. If the geodesic is nonseparating then the Jacobian degenerates. The aim of this work is to get insight into this process and give estimates in

    更新日期:2020-08-18
  • Tian’s $$\alpha _{m,k}^{{\hat{K}}}$$ α m , k K ^ -invariants on group compactifications
    Math. Z. (IF 0.881) Pub Date : 2020-08-17
    Yan Li, Xiaohua Zhu

    In this paper, we compute Tian’s \(\alpha _{m,k}^{K\times K}\)-invariant on a polarized G-group compactification, where K denotes a maximal compact subgroup of a connected complex reductive group G. We prove that Tian’s conjecture (see Conjecture 1.1 below) is true for \(\alpha _{m,k}^{K\times K}\)-invariant on such manifolds when \(k=1\), but it fails in general by producing counter-examples when

    更新日期:2020-08-17
  • On the Geometric Subgroups of the Étale Fundamental Groups of Varieties over Real Closed Fields
    Math. Z. (IF 0.881) Pub Date : 2020-08-12
    Yuichiro Hoshi, Takahiro Murotani, Shota Tsujimura

    In the present paper, we establish a “group-theoretic” algorithm for reconstructing, from the étale fundamental group of a suitable proper normal variety over a real closed field, the geometric subgroup of the étale fundamental group of the proper normal variety.

    更新日期:2020-08-12
  • Cluster algebras arising from cluster tubes I: integer vectors
    Math. Z. (IF 0.881) Pub Date : 2020-08-12
    Changjian Fu, Shengfei Geng, Pin Liu

    We study cluster algebras arising from cluster tubes. We obtain categorical interpretations for g-vectors, c-vectors and denominator vectors for cluster algebras of type \(\mathrm {C}\) with respect to arbitrary initial seeds. In particular, a denominator theorem has been proved, which enables us to establish the linearly independence of denominator vectors of cluster variables from the same cluster

    更新日期:2020-08-12
  • A dynamical dimension transference principle for dynamical diophantine approximation
    Math. Z. (IF 0.881) Pub Date : 2020-08-11
    Bao-Wei Wang, Guo-Hua Zhang

    Diophantine approximation in dynamical systems concerns the Diophantine properties of the orbits. In classic Diophantine approximation, the powerful mass transference principle established by Beresnevich and Velani provides a general principle to the dimension for a limsup set. In this paper, we aim at finding a general principle for the dimension of the limsup set arising in a general expanding dynamical

    更新日期:2020-08-11
  • Structure constants for Chern classes of Schubert cells
    Math. Z. (IF 0.881) Pub Date : 2020-08-11
    Changjian Su

    A formula for the structure constants of the multiplication of Schubert classes is obtained in (Rebecca and Allen. arXiv preprint arXiv:1909.05283, 2019). In this note, we prove analogous formulae for the Chern–Schwartz–MacPherson (CSM) classes and Segre–Schwartz–MacPherson (SSM) classes of Schubert cells in the flag variety. By the equivalence between the CSM classes and the stable basis elements

    更新日期:2020-08-11
  • An algebraic model for rational naïve-commutative ring SO (2)-spectra and equivariant elliptic cohomology
    Math. Z. (IF 0.881) Pub Date : 2020-08-10
    David Barnes, J. P. C. Greenlees, Magdalena Kędziorek

    Equipping a non-equivariant topological \(\text {E}_\infty \)-operad with the trivial G-action gives an operad in G-spaces. For a G-spectrum, being an algebra over this operad does not provide any multiplicative norm maps on homotopy groups. Algebras over this operad are called naïve-commutative ring G-spectra. In this paper we take \(G=SO(2)\) and we show that commutative algebras in the algebraic

    更新日期:2020-08-10
  • Motivic Tambara functors
    Math. Z. (IF 0.881) Pub Date : 2020-08-09
    Tom Bachmann

    Let k be a field and denote by \(\mathcal {SH}(k)\) the motivic stable homotopy category. Recall its full subcategory \(\mathcal {SH}(k)^{{\text {eff}}\heartsuit }\) (Bachmann in J Topol 10(4):1124–1144. arXiv:1610.01346, 2017). Write \(\mathrm {NAlg}(\mathcal {SH}(k))\) for the category of \({\mathrm {S}\mathrm {m}}\)-normed spectra (Bachmann-Hoyois in arXiv:1711.03061, 2017); recall that there is

    更新日期:2020-08-10
  • Exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds
    Math. Z. (IF 0.881) Pub Date : 2020-08-09
    Werner Müller, Frédéric Rochon

    For \(d=2n+1\) a positive odd integer, we consider sequences of arithmetic subgroups of \({\text {SO}}_0(d,1)\) and yielding corresponding hyperbolic manifolds of finite volume and show that, under appropriate and natural assumptions, the torsion of the associated cohomology groups grows exponentially.

    更新日期:2020-08-10
  • On the modularity of 2-adic potentially semi-stable deformation rings
    Math. Z. (IF 0.881) Pub Date : 2020-08-09
    Shen-Ning Tung

    Using p-adic local Langlands correspondence for \({\text {GL}}_2(\mathbb {Q}_2)\) and an ordinary \(R = \mathbb {T}\) theorem, we prove that the support of patched modules for quaternionic forms meet every irreducible component of the potentially semi-stable deformation ring. This gives a new proof of the Breuil–Mézard conjecture for 2-dimensional representations of the absolute Galois group of \(\mathbb

    更新日期:2020-08-10
  • Metrisability of projective surfaces and pseudo-holomorphic curves
    Math. Z. (IF 0.881) Pub Date : 2020-08-08
    Thomas Mettler

    We show that the metrisability of an oriented projective surface is equivalent to the existence of pseudo-holomorphic curves. A projective structure \({\mathfrak {p}}\) and a volume form \(\sigma \) on an oriented surface M equip the total space of a certain disk bundle \(Z\rightarrow M\) with a pair \((J_{{\mathfrak {p}}},{\mathfrak {J}}_{{\mathfrak {p}},\sigma })\) of almost complex structures. A

    更新日期:2020-08-09
  • Tower power for S -adics
    Math. Z. (IF 0.881) Pub Date : 2020-08-08
    Nicolas Bédaride, Arnaud Hilion, Martin Lustig

    We explain and restate the results from our recent paper [2] in standard language for substitutions and S-adic systems in symbolic dynamics. We then produce as rather direct application an S-adic system (with finite set of substitutions S on d letters) that is minimal and has d distinct ergodic probability measures. As second application we exhibit a formula that allows an efficient practical computation

    更新日期:2020-08-09
  • Gelfand-type theorems for dynamical Banach modules
    Math. Z. (IF 0.881) Pub Date : 2020-08-08
    Henrik Kreidler, Sita Siewert

    The representation theorems of Gelfand and Kakutani for commutative C*-algebras and AM- and AL-spaces are the basis for the Koopman linearization of topological and measure-preserving dynamical systems. In this article we prove versions of these results for dynamics on topological and measurable Banach bundles and the corresponding weighted Koopman representations on Banach modules.

    更新日期:2020-08-08
  • Birational sheets in reductive groups
    Math. Z. (IF 0.881) Pub Date : 2020-08-07
    Filippo Ambrosio

    We define the group analogue of birational sheets, a construction performed by Losev for reductive Lie algebras. For G semisimple simply connected, we describe birational sheets in terms of Lusztig–Spaltenstein induction and we prove that they form a partition of G, and that they are unibranch varieties with smooth normalization by means of a local study.

    更新日期:2020-08-08
  • Infinitesimally tight Lagrangian orbits
    Math. Z. (IF 0.881) Pub Date : 2020-08-07
    Elizabeth Gasparim, Luiz A. B. San Martin, Fabricio Valencia

    We describe isotropic orbits for the restricted action of a subgroup of a Lie group acting on a symplectic manifold by Hamiltonian symplectomorphisms and admitting an Ad*-equivariant moment map. We obtain examples of Lagrangian orbits of complex flag manifolds, of cotangent bundles of orthogonal Lie groups, and of products of flags. We introduce the notion of infinitesimally tight and study the intersection

    更新日期:2020-08-08
  • Some remarks on Hermitian manifolds satisfying Kähler-like conditions
    Math. Z. (IF 0.881) Pub Date : 2020-08-07
    Anna Fino, Nicoletta Tardini

    We study Hermitian metrics whose Bismut connection \(\nabla ^B\) satisfies the first Bianchi identity in relation to the SKT condition and the parallelism of the torsion of the Bimut connection. We obtain a characterization of complex surfaces admitting Hermitian metrics whose Bismut connection satisfy the first Bianchi identity and the condition \(R^B(x,y,z,w)=R^B(Jx,Jy,z,w)\), for every tangent vectors

    更新日期:2020-08-08
  • Local-global principles for norm one tori over semi-global fields
    Math. Z. (IF 0.881) Pub Date : 2020-08-06
    Sumit Chandra Mishra

    Let K be a complete discretely valued field with the residue field \(\kappa \). Let F be the function field of a smooth, projective, geometrically integral curve over K and \(\mathscr {X}\) be a regular proper model of F such that the reduced special fibre X is a union of regular curves with normal crossings. Suppose that the graph associated to \(\mathscr {X}\) is a tree (e.g. \(F = K(t)\)). Let L/F

    更新日期:2020-08-06
  • Tropical theta functions and Riemann–Roch inequality for tropical Abelian surfaces
    Math. Z. (IF 0.881) Pub Date : 2020-08-04
    Ken Sumi

    We show that the space of theta functions on tropical tori is identified with a convex polyhedron. We also show a Riemann-Roch inequality for tropical abelian surfaces by calculating the self-intersection numbers of divisors.

    更新日期:2020-08-04
  • On transfer maps in the algebraic K -theory of spaces
    Math. Z. (IF 0.881) Pub Date : 2020-07-25
    George Raptis

    We show that the Waldhausen trace map \(\mathrm {Tr}_X :A(X) \rightarrow QX_+\), which defines a natural splitting map from the algebraic K-theory of spaces to stable homotopy, is natural up to weak homotopy with respect to transfer maps in algebraic K-theory and Becker-Gottlieb transfer maps respectively.

    更新日期:2020-07-25
  • Serre–Tate theory for Shimura varieties of Hodge type
    Math. Z. (IF 0.881) Pub Date : 2020-07-15
    Ananth N. Shankar, Rong Zhou

    We study the formal neighbourhood of a point in the \(\mu \)-ordinary locus of an integral model of a Hodge type Shimura variety. We show that this formal neighbourhood has a structure of a “shifted cascade”. Moreover we show that the CM points on the formal neighbourhood are dense and that the identity section of the shifted cascade corresponds to a lift of the abelian variety which has a characterization

    更新日期:2020-07-15
  • An energy gap phenomenon for the Whitney sphere
    Math. Z. (IF 0.881) Pub Date : 2020-07-15
    Liuyang Zhang

    In this paper, we study Lagrangian surfaces satisfying \(\nabla ^*T=0\) , where \(T=-2\nabla ^*(\check{A}\lrcorner \omega )\) and \(\check{A}\) is the Lagrangian trace-free second fundamental form. We obtain a gap lemma for such a Lagrangian surface.

    更新日期:2020-07-15
  • t-Stabilities for a weighted projective line
    Math. Z. (IF 0.881) Pub Date : 2020-07-13
    Shiquan Ruan, Xintian Wang

    The present paper focuses on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the finest t-stabilities on certain triangulated category and, describe the semistable subcategories and last HN-triangles for coherent sheaves in \(D^b(\mathrm{coh\,}{{\mathbb {X}}})\), which is the bounded derived category of coherent

    更新日期:2020-07-13
  • Mixed norm Strichartz-type estimates for hypersurfaces in three dimensions
    Math. Z. (IF 0.881) Pub Date : 2020-07-12
    Ljudevit Palle

    In their work Ikromov and Müller (Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra. Princeton University Press, Princeton, 2016) proved the full range \(L^p-L^2\) Fourier restriction estimates for a very general class of hypersurfaces in \({\mathbb {R}}^3\) which includes the class of real analytic hypersurfaces. In this article we partly extend their results to the mixed

    更新日期:2020-07-13
  • Rigidity theorems for special Lagrangian cones
    Math. Z. (IF 0.881) Pub Date : 2020-07-11
    Caiyan Li

    In this paper, we derive that every n-dimensional (\(2\le n\le 7\)) special Lagrangian cones in \({\mathbb {R}}^{n}\times {\mathbb {R}}^{n}\) with flat normal bundle must be flat. And we also derive a rigidity result under a certain restriction on Gauss map.

    更新日期:2020-07-13
  • Theta lifts for Lorentzian lattices and coefficients of mock theta functions
    Math. Z. (IF 0.881) Pub Date : 2020-07-09
    Jan Hendrik Bruinier, Markus Schwagenscheidt

    We evaluate regularized theta lifts for Lorentzian lattices in three different ways. In particular, we obtain formulas for their values at special points involving coefficients of mock theta functions. By comparing the different evaluations, we derive recurrences for the coefficients of mock theta functions, such as Hurwitz class numbers, Andrews’ spt-function, and Ramanujan’s mock theta functions

    更新日期:2020-07-09
  • Generic representations of metaplectic groups and their theta lifts
    Math. Z. (IF 0.881) Pub Date : 2020-07-08
    Petar Bakić, Marcela Hanzer

    In this paper we give the description of generic representations of metaplectic groups over p-adic fields in terms of their Langlands parameters and calculate their theta lifts on all levels for any tower of odd orthogonal groups. We also describe precisely all the occurrences of the failure of the standard module conjecture for metaplectic groups.

    更新日期:2020-07-08
  • A liouville theorem on the PDE $$\det (f_{i\bar{\jmath }})=1$$ det ( f i ȷ ¯ ) = 1
    Math. Z. (IF 0.881) Pub Date : 2020-07-08
    An-Min Li, Li Sheng

    Let f be a smooth plurisubharmonic function which solves $$\begin{aligned} \det (f_{i\bar{\jmath }})=1\;\;\;\;\;\;\text{ on } \;\;\;\mathbb C^n. \end{aligned}$$ Suppose that the metric \(\omega _{f}=\sqrt{-1}f_{i\bar{\jmath }}dz_{i}\wedge d\bar{z}_{j}\) is complete and f satisfies the growth condition $$\begin{aligned} \mathsf N_{0}^{-1}(1+|z|^2)\le f\le \mathsf N_{0}(1+ |z|^2),\;\;\;\; \text{ as }\;\;\;

    更新日期:2020-07-08
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