GENERIC VANISHING THEORY VIA MIXED HODGE MODULES
نویسندگان
چکیده
منابع مشابه
Generic Vanishing Theory via Mixed Hodge Modules
We extend most of the results of generic vanishing theory to bundles of holomorphic forms and rank-one local systems, and more generally to certain coherent sheaves of Hodge-theoretic origin associated with irregular varieties. Our main tools are Saito’s mixed Hodge modules, the Fourier–Mukai transform for D-modules on abelian varieties introduced by Laumon and Rothstein, and Simpson’s harmonic...
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The term “generic vanishing” refers to a collection of theorems about the cohomology of line bundles with trivial first Chern class. The first results of this type were obtained by Green and Lazarsfeld in the late 1980s [13, 14]; they were proved using classical Hodge theory and are therefore valid on arbitrary compact Kähler manifolds. About ten years ago, Hacon [15] found a more algebraic app...
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This paper is an extended version of an expository talk given at the workshop “Topology of Stratified Spaces” at MSRI in September 2008. It gives an introduction and overview about recent developments on the interaction of the theories of characteristic classes and mixed Hodge theory for singular spaces in the complex algebraic context. It uses M. Saito’s deep theory of mixed Hodge modules as a...
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ژورنال
عنوان ژورنال: Forum of Mathematics, Sigma
سال: 2013
ISSN: 2050-5094
DOI: 10.1017/fms.2013.1