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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Hodge modules on complex tori and generic vanishing for compact Kähler manifolds

Giuseppe Pareschi, Mihnea Popa and Christian Schnell

Geometry & Topology 21 (2017) 2419–2460
Abstract

We extend the results of generic vanishing theory to polarizable real Hodge modules on compact complex tori, and from there to arbitrary compact Kähler manifolds. As applications, we obtain a bimeromorphic characterization of compact complex tori (among compact Kähler manifolds), semipositivity results and a description of the Leray filtration for maps to tori.

Keywords
generic vanishing, complex torus, Hodge modules, Kähler manifold
Mathematical Subject Classification 2010
Primary: 14C30
Secondary: 14F17
References
Publication
Received: 3 March 2016
Accepted: 8 October 2016
Published: 19 May 2017
Proposed: Richard Thomas
Seconded: Jim Bryan, Dan Abramovich
Authors
Giuseppe Pareschi
Dipartimento di Matematica
Università di Roma “Tor Vergata”
Via Della Ricerca Scientifica
I-00133 Roma
Italy
Mihnea Popa
Department of Mathematics
Northwestern University
2033 Sheridan Road
Evanston, IL 60208
United States
Christian Schnell
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794
United States