Generators for the cohomology ring of the moduli of one-dimensional sheaves on $\mathbb{P}^2$

TL;DR

This paper identifies a minimal set of generators for the cohomology and Chow rings of the moduli space of stable 1-dimensional sheaves on b2, advancing understanding of its algebraic structure.

Contribution

It provides a minimal generating set for the cohomology and Chow rings of the moduli space, using geometric methods to study tautological relations.

Findings

Established a minimal set of tautological generators.

Proved optimal generation results for cohomology and Chow rings.

Developed a geometric approach to tautological relations.

Abstract

We explore the structure of the cohomology ring of the moduli space of stable 1-dimensional sheaves on $\mathbb{P}^2$ of any degree. We obtain a minimal set of tautological generators, which implies an optimal generation result for both the cohomology and the Chow ring of the moduli space. Our approach is through a geometric study of tautological relations.