Birational models of moduli spaces of coherent sheaves on the projective plane

TL;DR

This paper investigates the birational geometry of moduli spaces of semistable sheaves on the projective plane using Bridgeland stability, revealing how wall-crossing describes their minimal model program and characterizing their movable cones.

Contribution

It provides a comprehensive description of the birational models of these moduli spaces via wall-crossing and describes their movable cones and chamber decompositions.

Findings

Wall-crossing describes the entire MMP of the moduli spaces.

The movable cone and chamber decomposition are explicitly characterized.

All birational models for primitive vectors are smooth and irreducible.

Abstract

We study the birational geometry of moduli spaces of semistable sheaves on the projective plane via Bridgeland stability conditions. We show that the entire MMP of their moduli spaces can be run via wall-crossing. Via a description of the walls, we give a numerical description of their movable cones, along with its chamber decomposition corresponding to minimal models. As an application, we show that for primitive vectors, all birational models corresponding to open chambers in the movable cone are smooth and irreducible.