Generic vanishing theory via mixed Hodge modules

Details Generic vanishing theory via mixed Hodge modules Generic vanishing theory via mixed Hodge modules

2011-12-13

arxiv.org/abs/1112.3058v2

Mathematics

Algebraic Geometry

48 pages; substantial changes involving a few new results and improved presentation

Scientific paper

We extend the dimension and strong linearity 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 to 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 discover two natural categories of perverse coherent sheaves, one on the Picard variety, and the other on the moduli space of Higgs line bundles or that of line bundles with flat connection.

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