Principal G-bundles over elliptic curves
Abstract
Let
G
be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal
G
bundles over an elliptic curve
E
. In particular we give a new proof of a theorem of Looijenga and Bernshtein-Shvartsman, that the moduli space is a weighted projective space. The method of proof is to study the deformations of certain unstable bundles coming from special maximal parabolic subgroups of
G
. We also discuss the associated automorphism sheaves and universal bundles, as well as the relation between various universal bundles and spectral covers.