Bridgeland/Weak Stability Conditions under Spherical Twist Associated to A Torsion Sheaf

TL;DR

This paper investigates how spherical twists, linked to torsion sheaves, influence Bridgeland stability conditions on K3 surfaces, leading to new stability constructions and insights into destabilizing objects.

Contribution

It provides a detailed analysis of autoequivalence actions on stability conditions and constructs a novel Bridgeland stability condition related to a non-nef divisor.

Findings

Construction of a Bridgeland stability condition for a non-nef divisor

Analysis of destabilizing objects under spherical twists

Discussion of stability of line bundles at weak stability conditions

Abstract

In this paper, we study the action of an autoequivalence, the spherical twist associated to a torsion sheaf, on the standard Bridgeland stability conditions and a generalized weak stability condition on the derived category of a K3 surface. As a special case, we construct a Bridgeland stability condition associated to a non-nef divisor, which conjecturally lies in the geometric component but outside the geometric chamber. We also discuss the destabilizing objects and stability of certain line bundles at the weak stability condition associated to a nef divisor.