• Math. Z. (IF 0.832) 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
• Math. Z. (IF 0.832) 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
• Math. Z. (IF 0.832) 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
• Math. Z. (IF 0.832) 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
• Math. Z. (IF 0.832) 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
• Math. Z. (IF 0.832) 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
• Math. Z. (IF 0.832) 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
• Math. Z. (IF 0.832) Pub Date : 2020-04-04

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
• Math. Z. (IF 0.832) 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
• Math. Z. (IF 0.832) 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
• Math. Z. (IF 0.832) 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
• Math. Z. (IF 0.832) Pub Date : 2019-09-13
Yuta Suzuki

In this paper, we consider pairs of a prime and a prime power with a fixed difference. We prove an average result on the distribution of such pairs. This is a partial improvement of the result of Bauer (Acta Arith. 85:99–118, 1998).

更新日期：2019-09-13
• Math. Z. (IF 0.832) Pub Date : 2019-09-05
Omer Offen

We study representations of the general and the special linear groups over a non-archimedean local field that admit a non-zero invariant linear form with respect to the symplectic group (henceforth distinguished representations). For the class of ladder representations that are distinguished we show that applying the highest derivative operation twice results in a distinguished (ladder) representation

更新日期：2019-09-05
• Math. Z. (IF 0.832) Pub Date : 2019-08-19
Ted Chinburg, Matthew Stover

Let X be a smooth geometrically irreducible projective surface over a field. In this paper we give an effective upper bound in terms of the Néron–Severi rank of X for the number of irreducible curves C on X with negative self-intersection and geometric genus less than $$b_1(X)/4$$, where $$b_1(X)$$ is the first étale Betti number of X. The proof involves a hyperbolic analog of the theory of spherical

更新日期：2019-08-19
• Math. Z. (IF 0.832) Pub Date : 2019-08-03
Marco Ramponi

We study a number of natural linear systems carried by any polarized Nikulin surface of genus g, determine their positivity and establish their Brill–Noether theory. As an application, we compute the classes of some natural effective divisors on the moduli space of Nikulin surfaces, relying upon recent work of Farkas and Rimányi.

更新日期：2019-08-03
• Math. Z. (IF 0.832) Pub Date : 2019-08-02
Yi-Hsuan Lin, Yifan Yang

Let $$\mathcal {Q}_D$$ be the set of moduli points on Siegel’s modular threefold whose corresponding principally polarized abelian surfaces have quaternionic multiplication by a maximal order $$\mathcal {O}$$ in an indefinite quaternion algebra of discriminant D over $$\mathbb {Q}$$ such that the Rosati involution coincides with a positive involution of the form $$\alpha \mapsto \mu ^{-1}\overline{\alpha 更新日期：2019-08-02 • Math. Z. (IF 0.832) Pub Date : 2019-08-02 Jinling Li, Chunhui Qiu In this paper, we first give several comparison theorems and their applications in Finsler geometry. Moreover, by means of the Hessian comparison theorems of a real Finsler manifold, Cartan connection, radial flag curvature and tangent curvature, we give Wu’s theorem on a strongly convex weakly Kähler Finsler manifold with a pole. Finally, by using the complex Rund connection and definition of radial 更新日期：2019-08-02 • Math. Z. (IF 0.832) Pub Date : 2019-08-01 Katrina Honigs, Luigi Lombardi, Sofia Tirabassi We prove that any Fourier–Mukai partner of an abelian surface over an algebraically closed field of positive characteristic is isomorphic to a moduli space of Gieseker-stable sheaves. We apply this fact to show that the set of Fourier–Mukai partners of a canonical cover of a hyperelliptic or Enriques surface over an algebraically closed field of characteristic greater than three is trivial. These results 更新日期：2019-08-01 • Math. Z. (IF 0.832) Pub Date : 2019-08-01 Kevin Coulembier We classify all equivalences between the indecomposable abelian categories which appear as blocks in BGG category \({\mathcal {O}}$$ for reductive Lie algebras. Our classification implies that a block in category $${\mathcal {O}}$$ only depends on the Bruhat order of the relevant parabolic quotient of the Weyl group. As part of the proof, we observe that any finite dimensional algebra with simple preserving

更新日期：2019-08-01
• Math. Z. (IF 0.832) Pub Date : 2019-07-09
Ananya Chaturvedi, Gordon Heier

The main result of this note essentially is that if the base and fibers of a compact fibration carry Hermitian metrics of positive holomorphic sectional curvature, then so does the total space of the fibration. The proof is based on the use of a warped product metric as in the work by Cheung in case of negative holomorphic sectional curvature, but differs in certain key aspects, e.g., in that it does

更新日期：2019-07-09
• Math. Z. (IF 0.832) Pub Date : 2019-07-05
Kohji Matsumoto, Tomokazu Onozuka, Isao Wakabayashi

We give explicit expressions (or at least an algorithm to obtain such expressions) of the coefficients of the Laurent series expansions of the Euler–Zagier multiple zeta-functions at any integer points. The main tools are the Mellin–Barnes integral formula and the harmonic product formulas. The Mellin–Barnes integral formula is used in the induction process on the number of variables, and the harmonic

更新日期：2019-07-05
• Math. Z. (IF 0.832) Pub Date : 2019-07-02
Aslak Bakke Buan, Henning Krause, Nicole Snashall, Øyvind Solberg

We provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category, where the tensor product is not necessarily symmetric. This is illustrated by examples, taken in particular from the representation theory of finite dimensional algebras.

更新日期：2019-07-02
• Math. Z. (IF 0.832) Pub Date : 2019-07-02
Baiying Liu, Gilbert Moss

In this paper, we prove an analogue of Jacquet’s conjecture on the local converse theorem for $$\ell$$-adic families of co-Whittaker representations of $${\mathrm {GL}}_n(F)$$, where F is a finite extension of $${\mathbb {Q}}_p$$ and $$\ell \ne p$$. We also prove an analogue of Jacquet’s conjecture for a descent theorem, which asks for the smallest collection of gamma factors determining the subring

更新日期：2019-07-02
• Math. Z. (IF 0.832) Pub Date : 2019-06-28
Thomas Gobet, Anne-Laure Thiel

We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by generators and relations. This ring turns out to be an extension of the Hecke algebra of the reflection group W and a free module of rank $$|W| (|W|-1)+1$$ over the

更新日期：2019-06-28
• Math. Z. (IF 0.832) Pub Date : 2019-06-27
Hailong Dao, Jonathan Montaño

Let R be a standard graded algebra over a field k, with irrelevant maximal ideal $$\mathfrak {m}$$, and I a homogeneous R-ideal. We study the asymptotic vanishing behavior of the graded components of the local cohomology modules $$\{{\text {H}}^{i}_{\mathfrak {m}}(R/I^n)\}_{n\in {\mathbb {N}}}$$ for $$i<\dim R/I$$. We show that, when $${{\,\mathrm{{{char}}}\,}}k= 0$$, R / I is Cohen–Macaulay, and I

更新日期：2019-06-27
• Math. Z. (IF 0.832) Pub Date : 2019-06-27
Scott Mullane

We exhibit infinitely many extremal effective codimension-k cycles in $$\overline{\mathcal {M}}_{g,n}$$ in the cases $$g\ge 3, n\ge g-1$$ and $$k=2$$, $$g\ge 2$$, $$k\le \min (n-g,g),$$ and $$g=1$$, $$k\le n-2$$. Hence in these cases the effective cone is not rational polyhedral.

更新日期：2019-06-27
• Math. Z. (IF 0.832) Pub Date : 2019-06-27
Chenyu Bai, Baohua Fu, Laurent Manivel

Complete intersections inside rational homogeneous varieties provide interesting examples of Fano manifolds. For example, if $$X = \cap _{i=1}^r D_i \subset G/P$$ is a smooth complete intersection of r ample divisors such that $$K_{G/P}^* \otimes {\mathcal O}_{G/P}(-\sum _i D_i)$$ is ample, then X is Fano. We first classify these Fano complete intersections which are locally rigid. It turns out that

更新日期：2019-06-27
• Math. Z. (IF 0.832) Pub Date : 2019-06-26
Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen, Jorge Lira

We study the asymptotic Dirichlet problem for Killing graphs with prescribed mean curvature H in warped product manifolds $$M\times _\varrho \mathbb {R}$$. In the first part of the paper, we prove the existence of Killing graphs with prescribed boundary on geodesic balls under suitable assumptions on H and the mean curvature of the Killing cylinders over geodesic spheres. In the process we obtain a

更新日期：2019-06-26
• Math. Z. (IF 0.832) Pub Date : 2019-06-26
Samir Bedrouni, David Marín

We show that up to automorphism of $${\mathbb {P}}^{2}_{{\mathbb {C}}}$$ there are 5 homogeneous convex foliations of degree four on $${\mathbb {P}}^{2}_{{\mathbb {C}}}.$$ Using this result, we give a partial answer to a question posed in 2013 by Marín and Pereira about the classification of reduced convex foliations on $${\mathbb {P}}^{2}_{{\mathbb {C}}}.$$

更新日期：2019-06-26
• Math. Z. (IF 0.832) Pub Date : 2019-06-25
Michal Hrbek

We classify all compactly generated t-structures in the unbounded derived category of an arbitrary commutative ring, generalizing the result of Alonso Tarrío et al. (J Algebra 324(3):313–346, 2010) for noetherian rings. More specifically, we establish a bijective correspondence between the compactly generated t-structures and infinite filtrations of the Zariski spectrum by Thomason subsets. Moreover

更新日期：2019-06-25
• Math. Z. (IF 0.832) Pub Date : 2019-06-25
Osamu Fujino, Wenfei Liu

We show that any union of slc strata of a Fano log pair with semi-log canonical singularities is simply connected. In particular, Fano log pairs with semi-log canonical singularities are simply connected, which confirms a conjecture of the first author.

更新日期：2019-06-25
• Math. Z. (IF 0.832) Pub Date : 2019-06-24
Xiaokui Yang

Let (X, g) be a compact Riemannian manifold with quasi-positive Riemannian scalar curvature. If there exists a complex structure J compatible with g, then the Kodaira dimension of (X, J) is equal to $$-\infty$$ and the canonical bundle $$K_X$$ is not pseudo-effective. We also introduce the complex Yamabe number $$\lambda _c(X)$$ for compact complex manifold X, and show that if $$\lambda _c(X)$$ is

更新日期：2019-06-24
• Math. Z. (IF 0.832) Pub Date : 2019-05-18
Eusebio Gardella, Hannes Thiel

We show that a representation of a Banach algebra A on a Banach space X can be extended to a canonical representation of $$A^{**}$$ on X if and only if certain orbit maps $$A\rightarrow X$$ are weakly compact. When this is the case, we show that the essential space of the representation is complemented if A has a bounded left approximate identity. This provides a tool to disregard the difference between

更新日期：2019-05-18
• Math. Z. (IF 0.832) Pub Date : 2019-05-16
Timothy C. Burness, Martin W. Liebeck, Aner Shalev

Let G be a connected Lie group. An unrefinable chain of G is defined to be a chain of subgroups $$G = G_0> G_1> \cdots > G_t = 1$$, where each $$G_i$$ is a maximal connected subgroup of $$G_{i-1}$$. In this paper, we introduce the notion of the length (respectively, depth) of G, defined as the maximal (respectively, minimal) length of such a chain, and we establish several new results for compact groups

更新日期：2019-05-16
• Math. Z. (IF 0.832) Pub Date : 2019-05-15
Julian Ahrens, Michael G. Cowling, Alessio Martini, Detlef Müller

A sharp $$L^p$$ spectral multiplier theorem of Mihlin–Hörmander type is proved for a distinguished sub-Laplacian on quaternionic spheres. This is the first such result on compact sub-Riemannian manifolds where the horizontal space has corank greater than one. The proof hinges on the analysis of the quaternionic spherical harmonic decomposition, of which we present an elementary derivation.

更新日期：2019-05-15
• Math. Z. (IF 0.832) Pub Date : 2019-05-14
Yoshishige Haraoka

We extend the middle convolution for monodromy of Fuchsian ordinary differential equations due to Katz to an operation for monodromy of KZ equations. This operation, also called the middle convolution, gives a monodromy of KZ equation obtained by the additive middle convolution. Since the fundamental group of the domain of definition of KZ equation is the pure braid group, our middle convolution also

更新日期：2019-05-14
• Math. Z. (IF 0.832) Pub Date : 2019-05-14
Yeongseong Jo

Let $$\pi$$ be an irreducible admissible representation of $$GL_m(F)$$, where F is a non-archimedean local field of characteristic zero. In 1990’s Jacquet and Shalika established an integral representation for the exterior square L-function. We complete, following the method developed by Cogdell and Piatetski-Shapiro, the computation of the local exterior square L-function $$L(s,\pi ,\wedge ^2)$$

更新日期：2019-05-14
• Math. Z. (IF 0.832) Pub Date : 2019-05-14
Khalid Bou-Rabee, Tasho Kaletha, Daniel Studenmund

Fixing a subgroup $$\varGamma$$ in a group G, the full commensurability growth function assigns to each n the cardinality of the set of subgroups $$\varDelta$$ of G with $$[\varGamma : \varGamma \cap \varDelta ][\varDelta : \varGamma \cap \varDelta ] \le n$$. For pairs $$\varGamma \le G$$, where G is a higher rank Chevalley group scheme defined over $${\mathbb {Z}}$$ and $$\varGamma$$ is an arithmetic

更新日期：2019-05-14
• Math. Z. (IF 0.832) Pub Date : 2019-05-13
Luis Hernández-Corbato, Francisco R. Ruiz del Portal, J. J. Sánchez-Gabites

In this paper we study the cohomological Conley index of arbitrary isolated invariant continua for continuous maps $$f :U \subseteq {\mathbb {R}}^d \rightarrow {\mathbb {R}}^d$$ by analyzing the topological structure of their unstable manifold. We provide a simple dynamical interpretation for the first cohomological Conley index, describing it completely, and relate it to the cohomological Conley index

更新日期：2019-05-13
• Math. Z. (IF 0.832) Pub Date : 2019-05-13
Cynthia Will

We construct many examples of Lie groups admitting a left-invariant metric of negative Ricci curvature. We study Lie algebras which are semidirect products $${\mathfrak {l}}= ({\mathfrak {a}} \oplus {\mathfrak {u}} ) < imes {\mathfrak {n}}$$ and we obtain examples where $${\mathfrak {u}}$$ is any semisimple compact real Lie algebra, $${\mathfrak {a}}$$ is one-dimensional and $${\mathfrak {n}}$$ is

更新日期：2019-05-13
• Math. Z. (IF 0.832) Pub Date : 2019-04-10
Haniya Azam, Shaheen Nazir, Muhammad Imran Qureshi

We describe the torus-equivariant cohomology of weighted partial flag orbifolds $${\mathrm {w}}\Sigma$$ of type A. We establish counterparts of several results known for the partial flag variety that collectively constitute what we refer to as “Schubert Calculus on $${\mathrm {w}}\Sigma$$ ”. For the weighed Schubert classes in $${\mathrm {w}}\Sigma$$, we give the Chevalley’s formula. In addition

更新日期：2019-04-10
• Math. Z. (IF 0.832) Pub Date : 2019-04-08
Anthony Poëls

We generalize the construction of Roy’s Fibonacci type numbers to the case of a Sturmian recurrence and we determine the classical exponents of approximation $$\omega _2(\xi )$$, $${\widehat{\omega }}_2(\xi )$$, $$\lambda _2(\xi )$$, $${\widehat{\lambda }}_2(\xi )$$ associated with these real numbers. This also extends similar results established by Bugeaud and Laurent in the case of Sturmian continued

更新日期：2019-04-08
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