Stability conditions on the canonical line bundle of $\mathbb{P}^3$

TL;DR

This paper investigates the stability conditions on the total space of the canonical line bundle over , constructing geometric and algebraic stability conditions, and employing spherical twists to explore the stability space.

Contribution

It introduces new geometric and algebraic stability conditions on the canonical bundle over , expanding understanding of stability spaces in this geometric context.

Findings

Constructed a family of geometric stability conditions.

Identified a subset of boundary stability conditions that are algebraic.

Used spherical twists to generate additional stability conditions.

Abstract

We study the space of stability conditions on the total space of the canonical line bundle over the three dimensional projective space. We construct a family of geometric stability conditions and some subset of the boudary of them, which are algebraic. We also use spherical twists to construct some other stability conditions.