Torus action on the moduli spaces of plane sheaves

TL;DR

This paper investigates the fixed points of a torus action on a moduli space of stable sheaves on the projective plane, computing topological invariants like Betti and Hodge numbers.

Contribution

It characterizes the torus fixed locus and determines tangent space representations, enabling the calculation of Betti and Hodge numbers for the moduli space.

Findings

Identified the torus fixed points on the moduli space.

Computed the Betti numbers of the moduli space.

Determined the Hodge numbers of the moduli space.

Abstract

We describe the torus fixed locus of the moduli space of stable sheaves with Hilbert polynomial $4m+1$ on the projective plane. We determine the torus representation of the tangent spaces at the fixed points, which leads to the computation of the Betti and Hodge numbers of the moduli space.