Principal G-bundles over elliptic curves

Details Principal G-bundles over elliptic curves Principal G-bundles over elliptic curves

1997-07-07

arxiv.org/abs/alg-geom/9707004v2

Math.Res.Lett.5:97-118,1998

Physics

High Energy Physics

High Energy Physics - Theory

AMS-TeX, 20 pages, amsppt style; minor errors corrected

Scientific paper

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.

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