The automorphism group of the moduli space of semi stable vector bundles

Abstract

Let $\mathcal{S}\mathcal{U}(r,L_0)$ denote the moduli space of semi stable vector bundles of rank $r$ and fixed determinant $L_0$ of degree $d$ on a smooth curve $C$ of genus $g\ge 3$. In this paper we describe the group of automorphisms of $\mathcal{S}\mathcal{U}(r,L_0)$. The analogue of this result is carried out for the space $\mathcal{U}(r,d)$ of semi stable vector bundles of rark $r$ and degree $d$. As an application of the technics we use, we give in the appendix at the end of the paper a proof of the Torelli theorem for the moduli spaces $\mathcal{S}\mathcal{U}(r,L_0)$ for any rank $r$ and degree $d$.

arXiv comment48 pages, LaTeX