Generalized parabolic sheaves on an integral projective curve

Abstract

We extend the notion of a parabolic vector bundle on a smooth curve to define generalized parabolic sheaves (GPS) on any integral projective curve X. We construct the moduli spaces M(X) of GPS of certain type on X. If X is obtained by blowing up finitely many nodes in Y then we show that there is a surjective birational morphism from M(X) to M(Y). In particular, we get partial desingularisations of the moduli of torsion-free sheaves on a nodal curve Y.