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GENERIC VANISHING THEORY VIA MIXED HODGE MODULES

  • MIHNEA POPA (a1) and CHRISTIAN SCHNELL (a2)
Abstract
Abstract

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 $\mathscr{D}$-modules on abelian varieties introduced by Laumon and Rothstein, and Simpson’s harmonic theory for flat bundles. In the process, we also discover two natural categories of perverse coherent sheaves.

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The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence <http://creativecommons.org/licenses/by/3.0/>.
Linked references
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

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Forum of Mathematics, Sigma
  • ISSN: -
  • EISSN: 2050-5094
  • URL: /core/journals/forum-of-mathematics-sigma
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