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作者：Paun, Mihai
作者单位：Universite de Lorraine
摘要：In this article we establish a very general non-vanishing statement, as well as several properties of metrics with minimal singularities of adjoint bundles. Our arguments combine the proof of the classical non-vanishing theorem due to V. Shokurov, as well as many ideas from Y.-T. Siu's analytic proof of the finite generation of the canonical ring. An important tool is the notion of relative critical exponent of two closed positive currents with respect to a measure.
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作者：Grushevsky, Samuel; Hulek, Klaus
作者单位：Leibniz University Hannover; State University of New York (SUNY) System; Stony Brook University
摘要：We study the locus of intermediate Jacobians of cubic threefolds within the moduli space of complex principally polarized abelian fivefolds, and its generalization to arbitrary genus-the locus of abelian varieties with a singular odd two-torsion point on the theta divisor. Assuming that this locus has expected codimension g (which we show to be true for ga parts per thousand currency sign5, and conjecturally for any g), we compute the class of this locus, and of its closure in the perfect cone...
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作者：Toen, Bertrand
作者单位：Universite de Montpellier
摘要：We introduce a notion of derived Azumaya algebras over ring and schemes generalizing the notion of Azumaya algebras of Grothendieck (Le groupe de Brauer. I. AlgSbres d'Azumaya et interpr,tations diverses. Dix Expos,s sur la Cohomologie des Sch,mas, pp. 46-66, North-Holland, Amsterdam, 1968). We prove that any such algebra B on a scheme X provides a class I center dot(B) in . We prove that for X a quasi-compact and quasi-separated scheme I center dot defines a bijective correspondence, and in p...
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作者：Andersson, Mats; Samuelsson, Hakan
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：Let X be a complex space of pure dimension. We introduce fine sheaves of (0,q)-currents, which coincides with the sheaves of smooth forms on the regular part of X, so that the associated Dolbeault complex yields a resolution of the structure sheaf . Our construction is based on intrinsic and quite explicit semi-global Koppelman formulas.
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作者：Lemou, Mohammed; Mehats, Florian; Raphael, Pierre
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Universite de Rennes; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We consider the three dimensional gravitational Vlasov Poisson system which is a canonical model in astrophysics to describe the dynamics of galactic clusters. A well known conjecture (Binney, Tremaine in Galactic Dynamics, Princeton University Press, Princeton, 1987) is the stability of spherical models which are nonincreasing radially symmetric steady states solutions. This conjecture was proved at the linear level by several authors in the continuation of the breakthrough work by Antonov (S...
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作者：Tran Vu Khanh; Zampieri, Giuseppe
作者单位：University of Padua
摘要：We show the geometric and analytic consequences of a general estimate in the (partial derivative) over bar -Neumann problem: a gain in the estimate yields a bound in the type of the boundary, that is, in its order of contact with an analytic curve as well as in the rate of the Bergman metric. We also discuss the potential-theoretical consequence: a gain implies a lower bound for the Levi form of a bounded weight.
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作者：Church, Thomas
作者单位：University of Chicago
摘要：Let C (n) (M) be the configuration space of n distinct ordered points in M. We prove that if M is any connected orientable manifold (closed or open), the homology groups H (i) (C (n) (M);ae) are representation stable in the sense of Church and Farb (arXiv:1008.1368). Applying this to the trivial representation, we obtain as a corollary that the unordered configuration space B (n) (M) satisfies classical homological stability: for each i, H (i) (B (n) (M); Q) approximate to H-i (B (n+1)(M); Q) ...
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作者：Guichard, Olivier; Wienhard, Anna
作者单位：Princeton University; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher Teichmuller spaces, and for lattices in SO(1,n). In this article we extend the notion of Anosov representations to representations of arbitrary word hyperbolic groups and start the systematic study of their geometric properties. In particular, given an Anos...
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作者：Abouzaid, Mohammed
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We prove that the inclusion of every closed exact Lagrangian with vanishing Maslov class in a cotangent bundle is a homotopy equivalence. We start by adapting an idea of Fukaya-Seidel-Smith to prove that such a Lagrangian is equivalent to the zero section in the Fukaya category with integral coefficients. We then study an extension of the Fukaya category in which Lagrangians equipped with local systems of arbitrary dimension are admitted as objects, and prove that this extension is generated, ...
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作者：Ballard, Matthew; Favero, David; Katzarkov, Ludmil
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Vienna
摘要：The Orlov spectrum is a new invariant of a triangulated category. It was introduced by D. Orlov, building on work of A. Bondal-M. Van den Bergh and R. Rouquier. The supremum of the Orlov spectrum of a triangulated category is called the ultimate dimension. In this work, we study Orlov spectra of triangulated categories arising in mirror symmetry. We introduce the notion of gaps and outline their geometric significance. We provide the first large class of examples where the ultimate dimension i...
