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

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.