Nef and Effective Cones on the Moduli Space of Torsion Sheaves on the Projective Plane

TL;DR

This paper investigates the divisor theory of the moduli space of semistable sheaves on the projective plane, establishing their Mori dream space property, calculating nef cones, and analyzing effective cones for various invariants.

Contribution

It proves these moduli spaces are Mori dream spaces, computes their nef cones, and determines conditions for isomorphism between different spaces.

Findings

All studied moduli spaces are Mori dream spaces.

Nef cones are explicitly calculated.

Effective cones are characterized for most invariants.

Abstract

In this paper, we study the divisor theory of the Simpson moduli space of semistable sheaves of dimension 1 on the projective plane. We prove that these spaces are all Mori dream spaces, and calculate their nef cones. We also study the effective cones of these spaces for most choices of numerical invariants. As a consequence, we work out precisely when two such spaces are isomorphic.