On the Rationality of Nagaraj-Seshadri Moduli Space

TL;DR

This paper proves that all irreducible components of the moduli space of rank 2 torsion-free sheaves with odd Euler characteristic on a reducible nodal curve are rational, revealing their geometric simplicity.

Contribution

It establishes the rationality of moduli components for a specific class of sheaves on reducible nodal curves, a new result in algebraic geometry.

Findings

All irreducible components are rational.

The moduli space components are geometrically simple.

The result applies to sheaves with odd Euler characteristic.

Abstract

We show that each of the irreducible components of moduli of rank 2 torsion-free sheaves with odd Euler characteristic over a reducible nodal curve is rational.