Moduli of rank one sheaves on P^2

This project will involve studying the moduli space of coherent sheaves on the projective plane that have one-dimensional support. This space has numerous nice topological properties, and its cohomology is amenable to direct computations via the study of tautological classes. Moreover, it has a presentation via noncommutative geometry, as a moduli space of certain representations over a particular quiver. In this project we will try to unite these ways of seeing this moduli space, to use recent techniques in algebraic geometry to recover fundamental properties of the moduli space.