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  • 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
  • Arithmetic of p -adic curves and sections of geometrically abelian fundamental groups
    Math. Z. (IF 0.881) Pub Date : 2020-07-04
    Mohamed Saïdi

    Let X be a proper, smooth, and geometrically connected curve of genus \(g(X)\ge 1\) over a p-adic local field. We prove that there exists an effectively computable open affine subscheme \(U\subset X\) with the property that \({\text {period}}(X)=1\), and \({\text {index}}(X)\) equals 1 or 2 (resp. \({\text {period}}(X)={\text {index}}(X)=1\), assuming \({\text {period}}(X)={\text {index}}(X)\)), if

    更新日期:2020-07-05
  • Twisted Fourier–Mukai partners of Enriques surfaces
    Math. Z. (IF 0.881) Pub Date : 2020-07-04
    Nicolas Addington, Andrew Wray

    Bridgeland and Maciocia showed that a complex Enriques surface X has no Fourier–Mukai partners apart from itself: that is, if \(D^b(X) \cong D^b(Y)\) then \(X \cong Y\). We extend this to twisted Fourier–Mukai partners: if \(\alpha \) is the non-trivial element of \({{\,\mathrm{Br}\,}}(X) = {\mathbb {Z}}/2\) and \(D^b(X,\alpha ) \cong D^b(Y,\beta )\), then \(X \cong Y\) and \(\beta \) is non-trivial

    更新日期:2020-07-05
  • Multiplicity one theorem for $$(\mathrm {GL}_{n+1},\mathrm {GL}_n)$$ ( GL n + 1 , GL n ) over a local field of positive characteristic
    Math. Z. (IF 0.881) Pub Date : 2020-07-03
    Dor Mezer

    Let \({\mathbb {F}}\) be a non-archimedean local field of characteristic different from 2. We consider distributions on \(\mathrm {GL}(n+1,{\mathbb {F}})\) which are invariant under the adjoint action of \(\mathrm {GL}(n,{\mathbb {F}})\). We prove that any such distribution is invariant under transposition. This implies that the restriction to \(\mathrm {GL}(n,{{\mathbb {F}}})\) of any irreducible

    更新日期:2020-07-03
  • KAM theory for the reversible perturbations of 2D linear beam equations
    Math. Z. (IF 0.881) Pub Date : 2020-07-03
    Chuanfang Ge, Jiansheng Geng, Zhaowei Lou

    In the present paper, we prove an infinite dimensional reversible Kolmogorov-Arnold-Moser (KAM) theorem. As an application, we study the existence of KAM tori for a class of two dimensional (2D) non-Hamiltonian completely resonant beam equations with derivative nonlinearities. The Birkhoff normal form theory is also used since there are no external parameters in the equations.

    更新日期:2020-07-03
  • Approximation in weighted Bergman spaces and Hankel operators on strongly pseudoconvex domains
    Math. Z. (IF 0.881) Pub Date : 2020-07-03
    Jinshou Gao, Zhangjian Hu

    Suppose D is a bounded strongly pseudoconvex domain in \({{\mathbb {C}}}^n\) with smooth boundary, and let \(\rho \) be its defining function. For \(1< p<\infty \) and \(\alpha >-1\), we show that the weighted Bergman projection \(P_\alpha \) is bounded on \(L^p(D, |\rho |^\alpha dV)\). With non-isotropic estimates for \(\overline{\partial }\) and Stein’s theorem on non-tangential maximal operators

    更新日期:2020-07-03
  • Waring–Goldbach problem involving cubes of primes
    Math. Z. (IF 0.881) Pub Date : 2020-07-03
    Tak Wing Ching, Kai Man Tsang

    It is widely conjectured that every sufficiently large integer satisfying certain necessary congruence conditions is the sum of 4 cubes of prime numbers. As an approximation to this conjecture, we shall establish two results in this paper. Firstly, we show that every large odd integer is the sum of a prime, 4 cubes of primes and 15 powers of 2. Secondly, we show that the conjecture is true for at least

    更新日期:2020-07-03
  • Extrinsic conformal lower bounds of eigenvalue for Dirac operator
    Math. Z. (IF 0.881) Pub Date : 2020-07-02
    Qun Chen, Linlin Sun

    In this note, we prove conformal lower bounds for Dirac operators of submanifolds in terms of conformal and extrinsic quantities.

    更新日期:2020-07-02
  • Hochschild cohomology and group actions
    Math. Z. (IF 0.881) Pub Date : 2020-07-02
    Alexander Perry

    Given a finite group action on a (suitably enhanced) triangulated category linear over a field, we establish a formula for the Hochschild cohomology of the category of invariants, assuming the order of the group is coprime to the characteristic of the base field. The formula shows that the cohomology splits canonically with one summand given by the invariant subspace of the Hochschild cohomology of

    更新日期:2020-07-02
  • A higher-order tangent map and a conjecture on the higher Nash blowup of curves
    Math. Z. (IF 0.881) Pub Date : 2020-07-02
    Enrique Chávez-Martínez, Daniel Duarte, Arturo Giles Flores

    We introduce a higher-order version of the tangent map of a morphism and find a matrix representation. We then apply this matrix to solve a conjecture by Yasuda regarding the semigroup of the higher Nash blowup of formal curves. We first show that the conjecture is true for toric curves. We conclude by exhibiting a family of non-monomial curves where the conjecture fails.

    更新日期:2020-07-02
  • Convergence of measures on compactifications of locally symmetric spaces
    Math. Z. (IF 0.881) Pub Date : 2020-07-01
    Christopher Daw, Alexander Gorodnik, Emmanuel Ullmo

    We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space \(S=\Gamma \backslash G/K\) is compact. More precisely, given a sequence of homogeneous probability measures on S, we expect that any weak limit is homogeneous with support contained in precisely one of the boundary components (including S itself). We introduce

    更新日期:2020-07-01
  • Measures of maximal entropy for suspension flows
    Math. Z. (IF 0.881) Pub Date : 2020-07-01
    Godofredo Iommi, Anibal Velozo

    We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any suspension flow defined over a sub-shift of finite type can be perturbed (by an arbitrarily small perturbation) so that the resulting flow has uncountably many ergodic

    更新日期:2020-07-01
  • A sharp exponent on sum of distance sets over finite fields
    Math. Z. (IF 0.881) Pub Date : 2020-07-01
    Doowon Koh, Thang Pham, Chun-Yen Shen, Le Anh Vinh

    We study a variant of the Erdős–Falconer distance problem in the setting of finite fields. More precisely, let E and F be sets in \(\mathbb {F}_q^d\), and \(\Delta (E), \Delta (F)\) be corresponding distance sets. We prove that if \(|E||F|\ge Cq^{d+\frac{1}{3}}\) for a sufficiently large constant C, then the set \(\Delta (E)+\Delta (F)\) covers at least a half of all distances. Our result in odd dimensional

    更新日期:2020-07-01
  • The Steinberg quotient of a tilting character
    Math. Z. (IF 0.881) Pub Date : 2020-07-01
    Paul Sobaje

    Let G be a simple algebraic group over an algebraically closed field of prime characteristic. If M is a finite dimensional G-module that is projective over the Frobenius kernel of G, then its character is divisible by the character of the Steinberg module. In this paper we study such quotients, showing that if M is an indecomposable tilting module, then the multiplicities of the orbit sums appearing

    更新日期:2020-07-01
  • Pseudo solutions, rotation sets, and shadowing rotations for monotone recurrence relations
    Math. Z. (IF 0.881) Pub Date : 2020-07-01
    Tong Zhou, Wen-Xin Qin

    By introducing for monotone recurrence relations pseudo solutions, which are analogues of pseudo orbits of dynamical systems, we show that for general monotone recurrence relations the rotation set is closed, and each element in the rotation set is realized by a Birkhoff orbit. Moreover, if there is an orbit without rotation number, then the system has positive topological entropy, and we can construct

    更新日期:2020-07-01
  • Bergman kernel and oscillation theory of plurisubharmonic functions
    Math. Z. (IF 0.881) Pub Date : 2020-06-30
    Bo-Yong Chen, Xu Wang

    Based on Harnack’s inequality and convex analysis we show that each plurisubharmonic function is locally BUO (bounded upper oscillation) with respect to polydiscs of finite type but not for arbitrary polydiscs. We also show that each function in the Lelong class is globally BUO with respect to all polydiscs. A dimension-free BUO estimate is obtained for the logarithm of the modulus of a complex polynomial

    更新日期:2020-06-30
  • Fenchel–Nielsen coordinates on the augmented moduli space of anti-de Sitter structures
    Math. Z. (IF 0.881) Pub Date : 2020-06-30
    Andrea Tamburelli

    In this paper we combine our recent work on regular globally hyperbolic maximal anti-de Sitter structures with the classical theory of globally hyperbolic maximal Cauchy-compact anti-de Sitter manifolds in order to define an augmented moduli space. Moreover, we introduce a coordinate system in this space that resembles the complex Fenchel–Nielsen coordinates for hyperbolic quasi-Fuchsian manifolds

    更新日期:2020-06-30
  • The Liouville theorem for $$p$$p -harmonic functions and quasiminimizers with finite energy
    Math. Z. (IF 0.881) Pub Date : 2020-06-24
    Anders Björn, Jana Björn, Nageswari Shanmugalingam

    We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite pth power energy in a (not necessarily complete) metric measure space equipped with a globally doubling measure supporting a global \(p\)-Poincaré inequality. The geometric conditions are that either (a) the measure has a sufficiently strong volume growth at infinity, or (b) the metric space is annularly

    更新日期:2020-06-25
  • Correction to: Kauffman type invariants for tied links
    Math. Z. (IF 0.881) Pub Date : 2020-06-19
    Francesca Aicardi, Jesús Juyumaya

    In the original publication, there are missing symbols in Theorem 1 and two missing lines in Theorem 3 (cf. https://arxiv.org/pdf/1607.04841v5.pdf).

    更新日期:2020-06-22
  • Conformal metric sequences with integral-bounded scalar curvature
    Math. Z. (IF 0.881) Pub Date : 2020-06-16
    Yuxiang Li, Zhipeng Zhou

    Let (M, g) be a smooth compact Riemiannian manifold without boundary and \(g_k\) be a metric conformal to g. Suppose \(\text{ vol }(M,g_k)+\Vert R_k\Vert _{L^p(M,g_k)}\frac{n}{2}\). We will use the 3-circles theorem to study the bubble tree convergence of \(g_k\).

    更新日期:2020-06-16
  • Twisted doubling integrals for classical groups
    Math. Z. (IF 0.881) Pub Date : 2020-06-16
    Yuanqing Cai

    We describe the twisted doubling integrals of Cai–Friedberg–Ginzburg–Kaplan in a conceptual way. This also extends the construction to the quaternionic unitary groups. We carry out the unfolding argument uniformly in this article. To do so, we define a family of degenerate Whittaker coefficients that are suitable in this setup and study some of their properties. We also prove certain related global

    更新日期:2020-06-16
  • Nonarchimedean components of non-endoscopic automorphic representations for quasisplit Sp ( N ) and O ( N )
    Math. Z. (IF 0.881) Pub Date : 2020-06-15
    Bin Xu

    Arthur classified the discrete automorphic representations of symplectic and orthogonal groups over a number field by that of the general linear groups. In this classification, those that are not from endoscopic lifting correspond to pairs \((\phi , b)\), where \(\phi \) is an irreducible unitary cuspidal automorphic representation of some general linear group and b is an integer. In this paper, we

    更新日期:2020-06-15
  • The $$RO(C_2)$$RO(C2) -graded cohomology of $$C_2$$C2 -surfaces in $$\underline{{\mathbb {Z}}/2}$$Z/2̲ -coefficients
    Math. Z. (IF 0.881) Pub Date : 2020-06-15
    Christy Hazel

    A surface with an involution can be viewed as a \(C_2\)-space where \(C_2\) is the cyclic group of order two. Up to equivariant isomorphism, all involutions on surfaces were classified in Bujalance et al. (Math Z 211:461–478, 1992) and recently classified using equivariant surgery in Dugger (J Homotopy Relat Struct 14(4):919–992, 2019). We use the classification given in Dugger (2019) to compute the

    更新日期:2020-06-15
  • Line bundles on rigid varieties and Hodge symmetry
    Math. Z. (IF 0.881) Pub Date : 2020-06-13
    David Hansen, Shizhang Li

    We prove several related results on the low-degree Hodge numbers of proper smooth rigid analytic varieties over non-archimedean fields. Our arguments rely on known structure theorems for the relevant Picard varieties, together with recent advances in p-adic Hodge theory. We also define a rigid analytic Albanese naturally associated with any smooth proper rigid space.

    更新日期:2020-06-13
  • Zero-one Schubert polynomials
    Math. Z. (IF 0.881) Pub Date : 2020-06-10
    Alex Fink, Karola Mészáros, Avery St. Dizier

    We prove that if \(\sigma \in S_m\) is a pattern of \(w \in S_n\), then we can express the Schubert polynomial \(\mathfrak {S}_w\) as a monomial times \(\mathfrak {S}_\sigma \) (in reindexed variables) plus a polynomial with nonnegative coefficients. This implies that the set of permutations whose Schubert polynomials have all their coefficients equal to either 0 or 1 is closed under pattern containment

    更新日期:2020-06-10
  • Homogeneous Levi non-degenerate hypersurfaces in $${{\mathbb {C}}}^3$$C3
    Math. Z. (IF 0.881) Pub Date : 2020-06-09
    Boris Doubrov, Alexandr Medvedev, Dennis The

    We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in \({{\mathbb {C}}}^3\) with symmetry algebra of dimension \(\ge 6\).

    更新日期:2020-06-09
  • On Lisbon integrals
    Math. Z. (IF 0.881) Pub Date : 2020-06-08
    Daniel Barlet, Teresa Monteiro Fernandes

    We introduce new complex analytic integral transforms, the Lisbon Integrals, which naturally arise in the study of the affine space \(\mathbb {C}^k\) of unitary polynomials \(P_s(z)\) where \(s\in \mathbb {C}^k\) and \(z\in \mathbb {C}\), \(s_i\) identified to the i-th symmetric function of the roots of \(P_s(z)\). We completely determine the \(\mathscr {D}\)-modules (or systems of partial differential

    更新日期:2020-06-08
  • Gamma factors for the Asai cube representation
    Math. Z. (IF 0.881) Pub Date : 2020-06-08
    Shih-Yu Chen

    We prove an equality between the gamma factors for the Asai cube representation of \(\mathrm{R}_{E/F}\mathrm{{GL}}_2\) defined by the Weil–Deligne representations and by the local zeta integrals of Ikeda and Piatetski-Shapiro–Rallis, where E is an étale cubic algebra over a local field F of characteristic zero.

    更新日期:2020-06-08
  • Existence of similar point configurations in thin subsets of $${\mathbb {R}}^d$$Rd
    Math. Z. (IF 0.881) Pub Date : 2020-06-05
    Allan Greenleaf, Alex Iosevich, Sevak Mkrtchyan

    We prove the existence of similar and multi-similar point configurations (or simplexes) in sets of fractional Hausdorff dimension in Euclidean space. Let \(d \ge 2\) and \(E\subset {{{\mathbb {R}}} }^d\) be a compact set. For \(k\ge 1\), define $$\begin{aligned} \Delta _k(E)=\left\{ \left( |x^1-x^2|, \dots , |x^i-x^j|,\dots , |x^k-x^{k+1}|\right) : \left\{ x^i\right\} _{i=1}^{k+1}\subset E\right\}

    更新日期:2020-06-05
  • On the Gan–Gross–Prasad problem for finite unitary groups
    Math. Z. (IF 0.881) Pub Date : 2020-06-05
    Dongwen Liu, Zhicheng Wang

    In this paper we study the Gan–Gross–Prasad problem for unitary groups over finite fields. Our results provide complete answers for unipotent representations, and we obtain the explicit branching of these representations.

    更新日期:2020-06-05
  • $$\mathbf {L^p\rightarrow L^q}$$Lp→Lq bounds for spherical maximal operators
    Math. Z. (IF 0.881) Pub Date : 2020-06-05
    T. Anderson, K. Hughes, J. Roos, A. Seeger

    Let \(f\in L^p({\mathbb {R}}^d)\), \(d\ge 3\), and let \(A_t f(x)\) be the average of f over the sphere with radius t centered at x. For a subset E of [1, 2] we prove close to sharp \(L^p\rightarrow L^q\) estimates for the maximal function \(\sup _{t\in E} |A_t f|\). A new feature is the dependence of the results on both the upper Minkowski dimension of E and the Assouad dimension of E. The result

    更新日期:2020-06-05
  • $$d\mathbb {Z}$$dZ -Cluster tilting subcategories of singularity categories
    Math. Z. (IF 0.881) Pub Date : 2020-06-05
    Sondre Kvamme

    For an exact category \({{\mathcal {E}}}\) with enough projectives and with a \(d\mathbb {Z}\)-cluster tilting subcategory, we show that the singularity category of \({{\mathcal {E}}}\) admits a \(d\mathbb {Z}\)-cluster tilting subcategory. To do this we introduce cluster tilting subcategories of left triangulated categories, and we show that there is a correspondence between cluster tilting subcategories

    更新日期:2020-06-05
  • On Tian–Todorov lemma and its applications to deformation of CR-structures
    Math. Z. (IF 0.881) Pub Date : 2020-06-04
    Sheng Rao, Yongpan Zou

    We give a new Tian–Todorov lemma on deformations of CR-structures and use it to reprove the deformation unobstructedness of normal compact strongly pseudoconvex CR-manifold under the assumption of \(d'd''\)-lemma, more faithfully following Tian–Todorov’s approach.

    更新日期:2020-06-04
  • Global regularity for 2D fractional magneto-micropolar equations
    Math. Z. (IF 0.881) Pub Date : 2020-06-03
    Haifeng Shang, Jiahong Wu

    The magneto-micropolar equations are important models in fluid mechanics and material sciences. This paper focuses on the global regularity problem on the 2D magneto-micropolar equations with fractional dissipation. We establish the global regularity for three important fractional dissipation cases. Direct energy estimates are not sufficient to obtain the desired global a priori bounds in each case

    更新日期:2020-06-03
  • Localization of the Kobayashi metric and applications
    Math. Z. (IF 0.881) Pub Date : 2020-06-03
    Jinsong Liu, Hongyu Wang

    In this paper we introduce a new class of domains— log-type convex domains, which have no boundary regularity assumptions. Then we will localize the Kobayashi metric in log-type convex subdomains. As an application, we prove a local version of continuous extension of rough isometric maps between two bounded domains with log-type convex Dini-smooth boundary points. Moreover we prove that the Teichmüller

    更新日期:2020-06-03
  • CR-invariance of the Steinness index
    Math. Z. (IF 0.881) Pub Date : 2020-06-03
    Jihun Yum

    We characterize the Diederich–Fornæss index and the Steinness index in terms of a special 1-form, which we call D’Angelo 1-form. We then prove that the Diederich–Fornæss and Steinness indices are invariant under CR-diffeomorphisms by showing CR-invariance of D’Angelo 1-forms.

    更新日期:2020-06-03
  • Completing perfect complexes
    Math. Z. (IF 0.881) Pub Date : 2020-04-13
    Henning Krause

    This note proposes a new method to complete a triangulated category, which is based on the notion of a Cauchy sequence. We apply this to categories of perfect complexes. It is shown that the bounded derived category of finitely presented modules over a right coherent ring is the completion of the category of perfect complexes. The result extends to non-affine noetherian schemes and gives rise to a

    更新日期:2020-04-13
  • On the centralizer of vector fields: criteria of triviality and genericity results
    Math. Z. (IF 0.881) Pub Date : 2020-04-10
    Martin Leguil, Davi Obata, Bruno Santiago

    In this paper we study the problem of knowing when the centralizer of a vector field is “small”. We obtain several criteria that imply different types of “small” centralizers, namely collinear, quasi-trivial and trivial. There are two types of results in the paper: general dynamical criteria that imply one of the “small” centralizers above; and genericity results about the centralizer. Some of our

    更新日期:2020-04-10
  • Counting tropical rational curves with cross-ratio constraints
    Math. Z. (IF 0.881) Pub Date : 2020-04-08
    Christoph Goldner

    We enumerate rational curves in toric surfaces passing through points and satisfying cross-ratio constraints using tropical and combinatorial methods. Our starting point is (Tyomkin in Adv Math 305:1356–1383, 2017), where a tropical-algebraic correspondence theorem was proved that relates counts of rational curves in toric varieties that satisfy point conditions and cross-ratio constraints to the analogous

    更新日期:2020-04-08
  • Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras
    Math. Z. (IF 0.881) Pub Date : 2020-04-06
    Chih-Whi Chen, Kevin Coulembier, Volodymyr Mazorchuk

    We prove that the tensor product of a simple and a finite dimensional \({\mathfrak {sl}}_n\)-module has finite type socle. This is applied to reduce classification of simple \({\mathfrak {q}}(n)\)-supermodules to that of simple \({\mathfrak {sl}}_n\)-modules. Rough structure of simple \({\mathfrak {q}}(n)\)-supermodules, considered as \({\mathfrak {sl}}_n\)-modules, is described in terms of the combinatorics

    更新日期:2020-04-06
  • Betti tables of MCM modules over the cone of a plane cubic
    Math. Z. (IF 0.881) Pub Date : 2020-04-04
    Alexander Pavlov

    We show that for maximal Cohen–Macaulay modules over the homogeneous coordinate ring of a smooth Calabi–Yau varieties X, the computation of Betti numbers can be reduced to computations of dimensions of certain \({\text {Hom}}\) spaces in the bounded derived category \(D^b(X)\). In the simplest case of a smooth elliptic curve E embedded in \({\mathbb {P}}^2\) as a smooth cubic, we get explicit values

    更新日期:2020-04-04
  • Derived invariants of the fixed ring of enveloping algebras of semisimple Lie algebras
    Math. Z. (IF 0.881) Pub Date : 2020-04-04
    Akaki Tikaradze

    Let \({\mathfrak {g}}\) be a semisimple complex Lie algebra, and let W be a finite subgroup of \({\mathbb {C}}\)-algebra automorphisms of the enveloping algebra \(U({\mathfrak {g}})\). We show that the derived category of \(U({\mathfrak {g}})^W\)-modules determines isomorphism classes of both \({\mathfrak {g}}\) and W. Our proofs are based on the geometry of the Zassenhaus variety of the reduction

    更新日期:2020-04-04
  • Spectral theory of a class of nilmanifolds attached to Clifford modules
    Math. Z. (IF 0.881) Pub Date : 2020-04-03
    Wolfram Bauer, Kenro Furutani, Chisato Iwasaki, Abdellah Laaroussi

    We determine the spectrum of the sub-Laplacian on pseudo H-type nilmanifolds and present pairs of isospectral but non-homeomorphic nilmanifolds with respect to the sub-Laplacian. We observe that these pairs are also isospectral with respect to the Laplacian. More generally, our method allows us to construct an arbitrary number of isospectral but mutually non-homeomorphic nilmanifolds. Finally, we present

    更新日期:2020-04-03
  • Dualizable and semi-flat objects in abstract module categories
    Math. Z. (IF 0.881) Pub Date : 2020-04-02
    Rune Harder Bak

    In this paper, we define what it means for an object in an abstract module category to be dualizable and we give a homological description of the direct limit closure of the dualizable objects. Our description recovers existing results of Govorov and Lazard, Oberst and Röhrl, and Christensen and Holm. When applied to differential graded modules over a differential graded algebra, our description yields

    更新日期:2020-04-02
  • A comparison of the real and non-archimedean Monge–Ampère operator
    Math. Z. (IF 0.881) Pub Date : 2020-04-02
    Christian Vilsmeier

    Let X be a proper algebraic variety over a non-archimedean, non-trivially valued field. We show that the non-archimedean Monge–Ampère measure of a metric arising from a convex function on an open face of some skeleton of \(X^{an }\) is equal to the real Monge–Ampère measure of that function up to multiplication by a constant. As a consequence we obtain a regularity result for solutions of the non-archimedean

    更新日期:2020-04-02
  • Uniqueness for the inverse boundary value problem with singular potentials in 2D
    Math. Z. (IF 0.881) Pub Date : 2019-12-05
    Emilia Blåsten, Leo Tzou, Jenn-Nan Wang

    In this paper we consider the inverse boundary value problem for the Schrödinger equation with potential in \(L^p\) class, \(p>4/3\). We show that the potential is uniquely determined by the boundary measurements.

    更新日期:2019-12-05
  • Constant length substitutions, iterated function systems and amorphic complexity
    Math. Z. (IF 0.881) Pub Date : 2019-11-22
    Gabriel Fuhrmann, Maik Gröger

    We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of the topological notion of amorphic complexity. For subshifts with discrete spectrum associated to constant length substitutions, this characterization allows us

    更新日期:2019-11-22
  • The Klein four slices of $$\Sigma ^n H\underline{{\mathbb {F}}}_2$$ Σ n H F ̲ 2
    Math. Z. (IF 0.881) Pub Date : 2019-11-18
    B. Guillou, C. Yarnall

    We describe the slices of positive integral suspensions of the equivariant Eilenberg–MacLane spectrum \(H\underline{{\mathbb {F}}_2}\) for the constant Mackey functor over the Klein four-group \(C_2\times C_2\).

    更新日期:2019-11-18
  • Moderately ramified actions in positive characteristic
    Math. Z. (IF 0.881) Pub Date : 2019-11-15
    Dino Lorenzini, Stefan Schröer

    In characteristic 2 and dimension 2, wild \({\mathbb Z}/2{{\mathbb {Z}}}\)-actions on k[[u, v]] ramified precisely at the origin were classified by Artin, who showed in particular that they induce hypersurface singularities. We introduce in this article a new class of wild quotient singularities in any characteristic \(p>0\) and dimension \(n\ge 2\) arising from certain non-linear actions of \({\mathbb

    更新日期:2019-11-15
  • Conformal blocks attached to twisted groups
    Math. Z. (IF 0.881) Pub Date : 2019-11-13
    Chiara Damiolini

    The aim of this paper is to generalize the notion of conformal blocks to the situation in which the Lie algebra they are attached to is replaced with a sheaf of Lie algebras depending on covering data of curves. The result is a vector bundle of finite rank on the stack \({\overline{{\mathcal {H}}\text {ur}}(\Gamma ,\xi )_{g, n}}\) parametrizing \(\Gamma \)-coverings of curves. Many features of the

    更新日期:2019-11-13
  • On the parabolic Harnack inequality for non-local diffusion equations
    Math. Z. (IF 0.881) Pub Date : 2019-11-11
    Dominik Dier, Jukka Kemppainen, Juhana Siljander, Rico Zacher

    We settle the open question concerning the Harnack inequality for globally positive solutions to non-local in time diffusion equations by constructing a counter-example for dimensions \(d\ge \beta \), where \(\beta \in (0,2]\) is the order of the equation with respect to the spatial variable. The equation can be non-local both in time and in space but for the counter-example it is important that the

    更新日期:2019-11-11
  • Remarks on Chern–Einstein Hermitian metrics
    Math. Z. (IF 0.881) Pub Date : 2019-11-08
    Daniele Angella, Simone Calamai, Cristiano Spotti

    We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.

    更新日期:2019-11-08
  • Purity in compactly generated derivators and t-structures with Grothendieck hearts
    Math. Z. (IF 0.881) Pub Date : 2019-11-07
    Rosanna Laking

    We study t-structures with Grothendieck hearts on compactly generated triangulated categories \({\mathcal {T}}\) that are underlying categories of strong and stable derivators. This setting includes all algebraic compactly generated triangulated categories. We give an intrinsic characterisation of pure triangles and the definable subcategories of \({\mathcal {T}}\) in terms of directed homotopy colimits

    更新日期:2019-11-07
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