Automorphisms of moduli spaces of vector bundles over a curve

TL;DR

This paper provides a new proof that the automorphism group of the moduli space of stable vector bundles over a smooth curve is generated by automorphisms of the curve, tensorizations, and dualizations under certain conditions.

Contribution

It offers a novel proof of the structure of automorphisms of moduli spaces of vector bundles, clarifying the generators of this automorphism group.

Findings

Automorphism group generated by curve automorphisms, tensorizations, and dualizations.

New proof technique for automorphism group structure.

Applicable for genus g ≥ 4 and specific rank and degree conditions.

Abstract

Let X be an irreducible smooth complex projective curve of genus g at least 4. Let M(r,\Lambda) be the moduli space of stable vector bundles over X or rank r and fixed determinant \Lambda, of degree d. We give a new proof of the fact that the automorphism group of M(r,\Lambda) is generated by automorphisms of the curve X, tensorization with suitable line bundles, and, if r divides 2d, also dualization of vector bundles.