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  • Localization of the Kobayashi metric and applications
    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
  • CR-invariance of the Steinness index
    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
  • Completing perfect complexes
    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
  • On the centralizer of vector fields: criteria of triviality and genericity results
    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
  • Counting tropical rational curves with cross-ratio constraints
    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
  • Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras
    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
  • Betti tables of MCM modules over the cone of a plane cubic
    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
  • Derived invariants of the fixed ring of enveloping algebras of semisimple Lie algebras
    Math. Z. (IF 0.832) 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 0.832) 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
  • Dualizable and semi-flat objects in abstract module categories
    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
  • A comparison of the real and non-archimedean Monge–Ampère operator
    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
  • On prime vs. prime power pairs
    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
  • On symplectic periods and restriction to SL (2 n )
    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
  • Negative curves of small genus on surfaces
    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
  • A note on Nikulin surfaces and their moduli spaces
    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
  • Quaternionic loci in Siegel’s modular threefold
    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
  • Comparison and Wu’s theorems in Finsler geometry
    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
  • Derived equivalences of canonical covers of hyperelliptic and Enriques surfaces in positive characteristic
    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
  • The classification of blocks in BGG category $${\mathcal {O}}$$O
    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
  • Hermitian metrics of positive holomorphic sectional curvature on fibrations
    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
  • Laurent series expansions of multiple zeta-functions of Euler–Zagier type at integer points
    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
  • Support varieties—an axiomatic approach
    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
  • On the local converse theorem and the descent theorem in families
    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
  • A Soergel-like category for complex reflection groups of rank one
    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
  • On asymptotic vanishing behavior of local cohomology
    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
  • On the effective cone of higher codimension cycles in $$\overline{\mathcal {M}}_{g,n}$$M¯g,n
    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
  • On Fano complete intersections in rational homogeneous varieties
    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
  • Asymptotic Dirichlet problems in warped products
    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
  • Convex foliations of degree 4 on the complex projective plane
    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
  • Compactly generated t-structures in the derived category of a commutative ring
    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
  • Simple connectedness of Fano log pairs with semi-log canonical singularities
    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
  • Scalar curvature, Kodaira dimension and $${{\widehat{A}}}$$A^ -genus
    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
  • Extending representations of Banach algebras to their biduals
    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
  • The length and depth of compact Lie groups
    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
  • Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres
    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
  • Multiplicative middle convolution for KZ equations
    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
  • Derivatives and exceptional poles of the local exterior square L -function for $$GL_m$$GLm
    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
  • Commensurability growths of algebraic groups
    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
  • Infinite series in cohomology: attractors and Conley index
    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
  • Negative Ricci curvature on some non-solvable Lie groups II
    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
  • The equivariant cohomology of weighted flag orbifolds
    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
  • Exponents of diophantine approximation in dimension 2 for numbers of Sturmian type
    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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