Degenerations of the moduli spaces of vector bundles on curves I

Abstract

Let Y be a smooth projective curve degenerating to a reducible curve X with two components meeting transversally at one point. We show that the moduli space of vector bundles of rank two and odd determinant on Y degenerates to a moduli space on X which has nice properties, in particular, it has normal crossings. We also show that a nice degeneration exists when we fix the determinant. We give some conjectures concerning the degeneration of moduli space of vector bundles on Y with fixed determinant and arbitrary rank.