Kodaira dimension and zeros of holomorphic one-forms


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.


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