The homology groups of certain moduli spaces of plane sheaves

TL;DR

This paper computes the additive homology groups and Hodge numbers of specific moduli spaces of semi-stable sheaves on the projective plane using the Bialynicki-Birula method, providing new topological insights.

Contribution

It determines the homology groups and Hodge numbers of certain moduli spaces of plane sheaves, a novel application of the Bialynicki-Birula method in this context.

Findings

Homology groups of the moduli spaces are explicitly determined.

Hodge numbers of the moduli spaces are computed.

Results provide new topological data for these moduli spaces.

Abstract

Using the Bialynicki-Birula method, we determine the additive structure of the integral homology groups of the moduli spaces of semi-stable sheaves on the projective plane having rank and Chern classes (5, 1, 4), (7, 2, 6), respectively, (0, 5, 19). We compute the Hodge numbers of these moduli spaces.