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作者：Bruinier, Jan Hendrik; Howard, Benjamin; Yang, Tonghai
作者单位：Technical University of Darmstadt; Boston College; University of Wisconsin System; University of Wisconsin Madison
摘要：We study special cycles on integral models of Shimura varieties associated with unitary similitude groups of signature . We construct an arithmetic theta lift from harmonic Maass forms of weight to the arithmetic Chow group of the integral model of a unitary Shimura variety, by associating to a harmonic Maass form a linear combination of Kudla-Rapoport divisors, equipped with the Green function given by the regularized theta lift of . Our main result is an equality of two complex numbers: (1) ...
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作者：Haissinsky, Peter
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We prove that the class of convex-cocompact Kleinian groups is quasi-isometrically rigid. We also establish that a word hyperbolic group with a planar boundary different from the sphere is virtually a convex-cocompact Kleinian group provided that its boundary has Ahlfors regular conformal dimension strictly less than 2 or if it acts geometrically on a CAT(0) cube complex.
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作者：Dobbins, Michael Gene
作者单位：Pohang University of Science & Technology (POSTECH)
摘要：Using equivariant topology, we prove that it is always possible to find points in the -dimensional faces of a -dimensional convex polytope so that their center of mass is a target point in . Equivalently, the -fold Minkowski sum of a -polytope's -skeleton is that polytope scaled by . This verifies a conjecture by Takeshi Tokuyama.
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作者：Guan, Qi'an; Zhou, Xiangyu
作者单位：Peking University; Peking University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences
摘要：In this article, stimulated by the effectiveness in Berndtsson's solution of the openness conjecture and continuing our solution of Demailly's strong openness conjecture, we discuss conditions to guarantee the effectiveness of the conjecture and establish such an effectiveness result. We explicitly point out a lower semicontinuity property of plurisubharmonic functions with a multiplier, which is implicitly contained in Guan and Zhou (2014, arXiv:1401.7158). We also obtain optimal effectivenes...
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作者：Charles, Francois
作者单位：Universite Paris Saclay
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作者：Langer, Adrian
作者单位：University of Warsaw
摘要：We prove Bogomolov's inequality for Higgs sheaves on varieties in positive characteristic p that can be lifted modulo p(2). This implies the Miyaoka-Yau inequality on surfaces of non-negative Kodaira dimension liftable modulo p(2). This result is a strong version of Shepherd-Barron's conjecture. Our inequality also gives the first algebraic proof of Bogomolov's inequality for Higgs sheaves in characteristic zero, solving the problem posed by Narasimhan.
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作者：Li, Wen-Wei
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
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作者：Crovisier, Sylvain; Pujals, Enrique R.
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We prove that any diffeomorphism of a compact manifold can be approximated in the topology by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (has a finite number of transitive hyperbolic attractors with open and dense basin of attraction).
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作者：Andersson, Mats; Wulcan, Elizabeth
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：We prove global effective versions of the Briancon-Skoda-Huneke theorem. Our results extend, to singular varieties, a result of Hickel on the membership problem in polynomial ideals in , and a related theorem of Ein and Lazarsfeld for smooth projective varieties. The proofs rely on known geometric estimates and new results on multivariable residue calculus.
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作者：Liu, Kefeng; Rao, Sheng; Yang, Xiaokui
作者单位：Zhejiang University; University of California System; University of California Los Angeles; Wuhan University; Northwestern University
摘要：We prove several formulas related to Hodge theory and the Kodaira-Spencer-Kuranishi deformation theory of Kahler manifolds. As applications, we present a construction of globally convergent power series of integrable Beltrami differentials on Calabi-Yau manifolds and also a construction of global canonical family of holomorphic -forms on the deformation spaces of Calabi-Yau manifolds. Similar constructions are also applied to the deformation spaces of compact Kahler manifolds.
