GENERIC VANISHING THEORY VIA MIXED HODGE MODULES

Mihnea Popa; Christian Schnell

doi:10.1017/fms.2013.1

GENERIC VANISHING THEORY VIA MIXED HODGE MODULES

Mihnea Popa, Christian Schnell

Mathematics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

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 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.

Original language	English (US)
Article number	e1
Journal	Forum of Mathematics, Sigma
Volume	1
DOIs	https://doi.org/10.1017/fms.2013.1
State	Published - Jan 1 2013

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Mathematics

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GENERIC VANISHING THEORY VIA MIXED HODGE MODULES

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