Generic Vanishing Fails for Surfaces in Positive Characteristic

Abstract

We show that there exist smooth surfaces violating Generic Vanishing in any characteristic $p\ge 3$. As a corollary, we recover a result of Hacon and Kovács, producing counterexamples to Generic Vanishing in dimension 3 and higher.

12 pages, Bollettino dell'Unione Matematica Italiana (2017)

References in corpus (1)

• Strong generic vanishing and a higher dimensional Castelnuovo-de Franchis inequality