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 spacesM(X) of GPS of certain type onX. IfX is obtained by blowing up finitely many nodes inY 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 curveY.
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