Kodaira dimension and zeros of holomorphic one-forms

Abstract

We show that every holomorphic one-form on a smooth complex projective variety of general type must vanish at some point. The proof uses generic vanishing theory for Hodge modules on abelian varieties.

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Authors

Mihnea Popa

Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607

Christian Schnell

Department of Mathematics, Stony Brook University, Stony Brook, NY 11794