Moduli of Bridgeland semistable objects on $\mathbb{P}^2$

TL;DR

This paper provides an alternative proof of classical results on moduli spaces of semistable sheaves on the projective plane using Bridgeland stability conditions and explores wall-crossing phenomena of Hilbert schemes.

Contribution

It offers a new proof of Le Potier's results and investigates wall-crossing in the context of Hilbert schemes via Bridgeland stability.

Findings

Alternative proof of Le Potier's result

Analysis of wall-crossing phenomena

Insights into moduli spaces of sheaves

Abstract

We give another proof of Le Potier's result and some variants on moduli spaces of semistable sheaves on the projective plane, using the Bridgeland stability conditions. As an application we study the wall-crossing phenomena of the Hilbert schemes of points on the projective plane.