Automorphisms of moduli spaces of symplectic bundles.

Abstract

Let X be an irreducible smooth complex projective curve of genus g >= 4. Fix a line bundle L on X. Let M-Sp (L) be the moduli space of semistable symplectic bundles (E,(sic) : E circle times E -> L) on X, with the symplectic form taking values in L. We show that the automorphism group of M-Sp (L) is generated by the automorphisms of the form E bar right arrow E circle times M, where M-2 congruent to O-X, together with the automorphisms induced by automorphisms of X.