# Generators of the cohomology ring, after Newstead

## TL;DR

This paper extends Newstead's description of the cohomology ring generators from smooth curves to irreducible nodal curves, showing they arise as degenerations of the smooth case generators.

## Contribution

It generalizes the known generators of the cohomology ring to the case of irreducible nodal curves, linking smooth and singular cases.

## Key findings

- Generators in the nodal case are natural degenerations of smooth case generators.
- The structure of the cohomology ring is preserved under degeneration from smooth to nodal curves.
- Provides a unified understanding of cohomology ring generators across different curve types.

## Abstract

Newstead gave the generators of the cohomology ring of the moduli space of rank 2 semi-stable, torsion-free sheaves with fixed odd degree determinant over a smooth, projective curve. In this article, we generalize this result to the case when the underlying curve is irreducible, nodal. We show that these generators (of the cohomology ring in the nodal curve case) arise naturally as degeneration of Newstead's generators in the smooth curve case.