The ample cone of moduli spaces of sheaves on the plane

TL;DR

This paper computes the ample cone of moduli spaces of sheaves on the plane using Bridgeland stability, extending previous results and covering new cases with specific rank and Chern class conditions.

Contribution

It applies recent Bridgeland stability results to explicitly determine the ample cone for certain moduli spaces of sheaves on the plane, generalizing earlier findings.

Findings

Explicit description of the ample cone for specified sheaves

Extension of previous results to new rank and Chern class cases

Recovery of classical results as special cases

Abstract

Fix a Chern character of a stable sheaf on the plane. Assume either the rank is at most 6 or the rank and first Chern class are coprime and the discriminant is sufficiently large. We use recent results of Bayer and Macri on Bridgeland stability to compute the ample cone of the moduli space of Gieseker semistable sheaves with the given Chern character. We recover earlier results, such as those by Stromme and Yoshioka, as special cases.