The Space of Stability Conditions on the Projective Plane

TL;DR

This paper explores the structure of the space of Bridgeland stability conditions on the derived category of coherent sheaves on the projective plane, revealing its decomposition and topological properties.

Contribution

It demonstrates that the principal component of the stability space is composed of geometric and algebraic parts, providing a cell decomposition and proving contractibility.

Findings

Stab^dag(P2) is the union of geometric and algebraic stability conditions.

The space admits a cell decomposition.

Stab^dag(P2) is contractible.

Abstract

The space of Bridgeland stability conditions on the bounded derived category of coherent sheaves on P2 has a principle connected component Stab^\dag(P2). We show that Stab^\dag(P2) is the union of geometric and algebraic stability conditions. As a consequence, we give a cell decomposition for Stab^\dag (P2) and show that Stab^\dag(P2) is contractible.