Moduli space of $G$-connections on an elliptic curve

Abstract

Let $X$ be a smooth complex elliptic curve and $G$ a connected reductive affine algebraic group defined over $\mathbb{C}$. Let ${\mathcal{M}}_X(G)$ denote the moduli space of topologically trivial algebraic $G$--connections on $X$, that is, pairs of the form $(E_G,D)$, where $E_G$ is a topologically trivial algebraic principal $G$--bundle on $X$, and $D$ is an algebraic connection on $E_G$. We prove that ${\mathcal{M}}_X(G)$ does not admit any nonconstant algebraic function while being biholomorphic to an affine variety.

Final version

References in corpus (1)

• Holomorphic principal bundles over elliptic curves