Hodge modules on complex tori and generic vanishing for compact Kähler manifolds

Giuseppe Pareschi; Mihnea Popa; Christian Schnell

doi:10.2140/gt.2017.21.2419

Hodge modules on complex tori and generic vanishing for compact Kähler manifolds

Giuseppe Pareschi, Mihnea Popa, Christian Schnell

Mathematics

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

5 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2419-2460
Number of pages	42
Journal	Geometry and Topology
Volume	21
Issue number	4
DOIs	https://doi.org/10.2140/gt.2017.21.2419
State	Published - May 19 2017

ASJC Scopus subject areas

Geometry and Topology

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title = "Hodge modules on complex tori and generic vanishing for compact K{\"a}hler manifolds",

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

author = "Giuseppe Pareschi and Mihnea Popa and Christian Schnell",

note = "Funding Information: During the preparation of this paper Schnell has been partially supported by the NSF grant DMS-1404947, Popa by the NSF grant DMS-1405516 and Pareschi by the MIUR PRIN project Geometry of algebraic varieties.",

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AU - Pareschi, Giuseppe

AU - Popa, Mihnea

AU - Schnell, Christian

N1 - Funding Information: During the preparation of this paper Schnell has been partially supported by the NSF grant DMS-1404947, Popa by the NSF grant DMS-1405516 and Pareschi by the MIUR PRIN project Geometry of algebraic varieties.

PY - 2017/5/19

Y1 - 2017/5/19

N2 - 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.

AB - 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.

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