Stability conditions on generic complex tori

TL;DR

This paper characterizes a specific connected component of stability conditions on the derived category of generic complex tori, providing explicit descriptions for all stability conditions within it.

Contribution

It offers the first explicit description of stability conditions on the derived category of generic complex tori, expanding understanding of their geometric and categorical structures.

Findings

Identifies a simply connected component of the stability manifold.

Provides explicit descriptions of all stability conditions in that component.

Focuses on generic complex tori with no nontrivial integral (p,p)-classes.

Abstract

In this paper we describe a simply connected component of the complex manifold of stability conditions on the bounded derived category of a generic complex torus of any dimension. A torus is called generic if there are no nontrivial integral (p,p)-classes. We give an explicit description of all stability conditions in that connected component.