Automorphisms of ${\mathbb C}^*$ Moduli Spaces Associated to a Riemann Surface

TL;DR

This paper determines the automorphism groups of various moduli spaces related to a compact Riemann surface, specifically for the multiplicative group ${ m C}^*$, providing insights into their symmetries.

Contribution

It explicitly computes the automorphism groups of Dolbeault, de Rham, and Betti moduli spaces for ${ m C}^*$ on a Riemann surface, a novel analysis in this context.

Findings

Automorphism groups of Dolbeault, de Rham, and Betti moduli spaces are explicitly characterized.

The structure of these automorphism groups reveals symmetries of the moduli spaces.

Results contribute to understanding the geometric and algebraic symmetries of moduli spaces associated with Riemann surfaces.

Abstract

We compute the automorphism groups of the Dolbeault, de Rham and Betti moduli spaces for the multiplicative group ${\mathbb C}^*$ associated to a compact connected Riemann surface.