Holomorphic principal bundles over elliptic curves

TL;DR

This paper classifies holomorphic principal G-bundles over elliptic curves, analyzes their moduli space, and identifies canonical representatives for semistable bundles, advancing understanding of their structure and automorphisms.

Contribution

It provides a classification of holomorphic principal G-bundles over elliptic curves and studies the structure of their moduli space, including canonical representatives.

Findings

Classification of holomorphic principal G-bundles over elliptic curves

Identification of canonical representatives for semistable G-bundles

Analysis of automorphism groups of these bundles

Abstract

In this paper, the first of a series of three, we classify holomorphic principal G-bundles over an elliptic curve, where G is a reductive group. We also study the local and global properties of the moduli space of semistable G-bundles. We identify canonical representatives for each S-equivalence class of semistable G-bundles, and study their automorphism groups.