Automorphisms of moduli spaces of symplectic bundle

TL;DR

This paper characterizes the automorphism group of the moduli space of symplectic bundles over a complex curve, showing it is generated by automorphisms from curve symmetries and 2-torsion line bundle twists.

Contribution

It provides a complete description of the automorphism group of the moduli space of symplectic bundles, linking it to curve automorphisms and line bundle torsion automorphisms.

Findings

Automorphism group generated by curve automorphisms and 2-torsion line bundle twists.

Automorphisms correspond to symmetries of the underlying curve and specific line bundle transformations.

The structure of the automorphism group is explicitly characterized.

Abstract

Let X be an irreducible smooth complex projective curve of genus at least 3. Fix a line bundle L on X. Let M_{Sp}(L) be the moduli space of symplectic bundles (E, ExE ---> L) on X, with the symplectic form taking values in L. We show that the automorphism group of M_{Sp}(L) is generated by automorphisms sending E to ExM, where M is a 2-torsion line bundle, and automorphisms induced by automorphisms of X.