A global description of the fine Simpson moduli space of 1-dimensional sheaves supported on plane quartics

Abstract

A global description of the fine Simpson moduli spaces of $1$-dimensional sheaves supported on plane quartics is given: we describe the gluing of the Brill-Noether loci described by Drézet and Maican and show that the Simpson moduli space $M=M_{4m\pm 1}({\mathbb{P}}_2)$ is a blow-down of a blow-up of a projective bundle over a smooth moduli space of Kronecker modules. An easy computation of the Poincaré polynomial of $M$ is presented.

An important reference added: Theorem 3.1 turns out to coincide with Theorem 3.1 from arXiv:1506.00298 [math.AG]. Our methods are however different

References in corpus (1)

• Torus action on the moduli spaces of plane sheaves