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

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

1993-06-02

arxiv.org/abs/alg-geom/9306001v1

Mathematics

Algebraic Geometry

48 pages, LaTeX

Scientific paper

Let ${\cal S}{\cal U}(r, L_0)$ 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 $g \geq 3$. In this paper we describe the group of automorphisms of $ {\cal S}{\cal U}(r, L_0) $. The analogue of this result is carried out for the space ${\cal 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 ${\cal S}{\cal U}(r, L_0) $ for any rank $r$ and degree $d$.

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