Moduli space of G-connections on an elliptic curve

2015/04/08 by Indranil Biswas, Biswas, Indranil
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1504.01821

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.

Citations

• Vector Bundles Over an Elliptic Curve

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