Bridgeland stability conditions on some higher-dimensional Calabi--Yau manifolds and generalized Kummer varieties

Abstract

We construct Bridgeland stability conditions on the the following hyper-K\"ahler or strict Calabi--Yau manifolds: - Generalized Kummer varieties associated to an abelian surface that is isogenous to a product of elliptic curves. - Universal covers of Hilbert schemes of some Enriques surfaces; this provides examples of stability conditions on strict Calabi--Yau manifolds in each even dimension. - Albanese fibers of some finite \'etale covering of Hilbert schemes of some bielliptic surfaces; this provides examples of stability conditions on strict Calabi-Yau manifolds in each odd dimension. - Cynk--Hulek Calabi--Yau manifolds with an automorphism of order $2$ or $3$.