Generic Vanishing for Singular Varieties via Du Bois complexes

TL;DR

This paper extends generic vanishing theorems to singular varieties using Du Bois complexes, providing a broader theoretical framework that explains previous counterexamples and generalizes classical results.

Contribution

It introduces new generic vanishing theorems for singular varieties based on Du Bois complexes, expanding the scope of classical vanishing theorems.

Findings

Generalizes classical generic vanishing theorems to singular varieties

Provides a theoretical explanation for previous counterexamples

Establishes a new framework using Du Bois complexes

Abstract

We prove appropriate generic vanishing theorems for singular varieties, generalizing the well-known generic vanishing theorem by Green and Lazarsfeld in [GL87] and the generic vanishing theorem of Nakano type in [PS13]. Our theorem explains the counterexample of Hacon and Kov\'acs in [HK15].