Chow ring of the moduli space of stable sheaves supported on quartic curves

TL;DR

This paper computes the Chow and cohomology rings of the moduli space of certain stable sheaves on the projective plane, providing key data for understanding BPS invariants and strange duality.

Contribution

It explicitly determines the Chow and cohomology rings of the moduli space of stable sheaves with Hilbert polynomial 4m+1 on the projective plane, a novel calculation in this context.

Findings

Computed the Chow ring of the moduli space

Derived the cohomology ring and total Chern class

Provided Euler characteristics for line bundles

Abstract

Motivated by the computation of the BPS-invariants on a local Calabi-Yau threefold suggested by S. Katz, we compute the Chow ring and the cohomology ring of the moduli space of stable sheaves of Hilbert polynomial $4m+1$ on the projective plane. As a byproduct, we obtain the total Chern class and Euler characteristics of all line bundles, which provide a numerical data for the strange duality on the plane.