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

Pareschi, Giuseppe¹ ; Popa, Mihnea² ; Schnell, Christian³

¹ Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via Della Ricerca Scientifica, I-00133 Roma, Italy
² Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, United States
³ Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, United States

Geometry & topology, Tome 21 (2017) no. 4, pp. 2419-2460.

Résumé

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.

Détail

DOI : 10.2140/gt.2017.21.2419

Classification : 14C30, 14F17
Keywords: generic vanishing, complex torus, Hodge modules, Kähler manifold

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