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GENERIC VANISHING THEORY VIA MIXED HODGE MODULES

Published online by Cambridge University Press:  17 May 2013

MIHNEA POPA
Affiliation:
Department of Mathematics, Statistics & Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607, USAmpopa@math.uic.edu
CHRISTIAN SCHNELL
Affiliation:
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USAcschnell@math.sunysb.edu

Abstract

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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.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence .
Copyright
© The Author(s) 2013.

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