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.

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

References in corpus (1)

• Vector Bundles And F Theory

Cited by in corpus (5)

• Moduli in N=1 heterotic/F-theory duality
• On Vector Bundles and Chiral Matter in N=1 Heterotic Compactifications
• Taniguchi Lecture on Principal Bundles on Elliptic Fibrations
• ICMP lecture on Heterotic/F-theory duality
• On discrete Twist and Four-Flux in N=1 heterotic/F-theory compactifications