Degenerations of the moduli spaces of vector bundles on curves II (generalized Gieseker moduli spaces)

Abstract

Let X₀ be a projective curve whose singularity is one ordinary double point. We construct a birational model G(n,d) of the moduli space U(n, d) of stable torsion free sheaves in the case (n,d)=1, such that G(n,d) has normal crossing singularities and behaves well under specialization i.e. if a smooth projective curve specializes to X₀, then the moduli space of stable vector bundles of rank n and degreed on X specializes to G(n,d). This generalizes an earlier work of Gieseker in the rank two case.