Elementary transformations and the rationality of the Moduli Spaces of Vector Bundles on ?2

Abstract

In this work, using elementary transformations and prioritary sheaves, we establish birational maps between certain moduli spaces of stable vector bundles over ℙ2 with the same rank and different Chern classes. As an application we give a simple proof of the rationality of the moduli spaces M(r; c 1, c 2) of rank r stable vector bundles over ℙ2 with given Chern classes for a huge families of the triples (r; c 1, c 2).