Derived equivalences of smooth stacks and orbifold Hodge numbers

TL;DR

This paper investigates how derived equivalences between orbifolds influence their orbifold Hodge numbers and Picard varieties, extending known results from smooth varieties to those with quotient singularities.

Contribution

It extends the understanding of derived equivalences to orbifolds with quotient singularities, revealing their impact on orbifold Hodge numbers and Picard varieties.

Findings

Derived equivalences preserve certain orbifold Hodge numbers.

Extensions of smooth case results to orbifolds with quotient singularities.

Implications for the structure of Picard varieties in orbifold settings.

Abstract

Given a derived equivalence of orbifolds associated to projective varieties with (not necessarily Gorenstein) quotient singularities, we deduce consequences related to the behavior of orbifold Hodge numbers and the Picard variety, extending what is known in the smooth case.