Rationality of moduli space of torsion-free sheaves over reducible curve

Abstract

Let M ( 2 , w ̲ , χ ) be the moduli space of rank 2 torsion-free sheaves of fixed determinant and odd Euler characteristic over a reducible nodal curve with each irreducible component having utmost two nodal singularities. We show that in each irreducible component of M ( 2 , w ̲ , χ ) , the closure of rank 2 vector bundles is rational.