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

TL;DR

This paper constructs Bridgeland stability conditions on various higher-dimensional Calabi--Yau and hyper-K"ahler manifolds, expanding the understanding of stability conditions in complex geometry.

Contribution

It provides explicit constructions of stability conditions on new classes of higher-dimensional Calabi--Yau manifolds and hyper-K"ahler varieties, including generalized Kummer and Cynk--Hulek types.

Findings

Examples of stability conditions on strict Calabi--Yau manifolds in all dimensions

Construction on generalized Kummer varieties associated to abelian surfaces

Stability conditions on Albanese fibers of certain Hilbert schemes

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 $3$.