Holomorphic Principal Bundles Over Elliptic Curves II: The Parabolic Construction

Abstract

This paper continues the study of holomorphic semistable principal G-bundles over an elliptic curve. In this paper, the moduli space of all such bundles is constructed by considering deformations of a minimally unstable G-bundle. The set of all such deformations can be described as the C^* quotient of the cohomology group of a sheaf of unipotent groups, and we show that this quotient has the structure of a weighted projective space. We identify this weighted projective space with the moduli space of semistable G-bundles, giving a new proof of a theorem of Looijenga.