On the homology of the moduli space of plane sheaves with Hilbert polynomial 5m+3

TL;DR

This paper calculates the Hodge numbers of a specific moduli space of semi-stable sheaves on the complex projective plane, focusing on sheaves supported on quintic curves with Euler characteristic 3, using torus action fixed points.

Contribution

It provides the first detailed computation of Hodge numbers for this class of moduli spaces, advancing understanding of their geometric structure.

Findings

Hodge numbers of the moduli space are explicitly computed.

The fixed-point set under torus action is characterized.

Results contribute to the classification of moduli spaces of sheaves.

Abstract

We compute the Hodge numbers of the moduli space of semi-stable sheaves on the complex projective plane supported on quintic curves and having Euler characteristic 3. For this purpose we study the fixed-point set for a certain torus action on the moduli space.