GENERIC VANISHING THEORY VIA MIXED HODGE MODULES

By Mihnea Cristian Popa, C. Schnell. Forum of Mathematics, Sigma, 2011

56 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f1593f5bdeb389d4e398c1b1dc5f248e16af7c97

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In Geometry and Topology

1. Nero Budur
2. Morihiko Saito

In Mathematical Physics

1. Nero Budur
2. Morihiko Saito

Citations in the corpus

• Bernstein-Sato ideals and local systems (2012, background): “n, Alexander module, Milnor fiber, Monodromy Conjecture, hyperplane arrangements. 1 2 NEROBUDUR [19, 20], Arapura [1, 2], Simpson [42], Budur [9], Libgober [27], Dimca-PapadimaSuciu [17], Popa-Schnell [37], Dimca-Papadima [16]. The union of the cohomology jump loci forms the cohomology support locus.”