On A Relative Mumford-Newstead Theorem

Abstract

In this paper we prove a relative version of the classical Mumford-Newstead theorem for a family of smooth curves degenerating to a reducible curve with a simple node. We also prove a Torelli-type theorem by showing that certain moduli spaces of torsion-free sheaves on a reducible curve allows us to recover the curve from the moduli space.

arXiv commentFinal version, 32 pages, to appear in Bulletin des Sciences mathemaquies