3:30 pm, Seminar Hall
Rationality of moduli space of torsion-free sheaves over a chain-like curve
Let C be a connected projective reducible nodal curve with each component having utmost two nodal singularities. Let M(2,w,X) be the moduli space of rank 2, semi-stable torsion-free sheaves over C with odd Euler characteristic X. Let L be a line bundle on C of "suitable" Euler characteristic. We show that the moduli space of stable vector bundles in M(2,w,X) with determinant L is a rational variety.
As a particular case, we prove the rationality of both the irreducible components of the Nagaraj-Seshadri moduli space with fixed determinant.