Derived equivalence and non-vanishing loci II

TL;DR

This paper investigates how derived equivalence affects cohomological support loci and Hodge numbers, providing new cases of invariance and exploring the behavior of fibrations over curves.

Contribution

It establishes specific cases of a conjecture linking derived equivalence with invariance of cohomological support loci and Hodge numbers, and studies derived behavior of fibrations over curves.

Findings

Proves new cases of invariance of cohomological support loci under derived equivalence.

Connects invariance of support loci with Hodge number invariance.

Analyzes derived behavior of fibrations over curves.

Abstract

We prove a few cases of a conjecture on the invariance of cohomological support loci under derived equivalence by establishing a concrete connection with the related problem of the invariance of Hodge numbers. We use the main case in order to study the derived behavior of fibrations over curves.