Holomorphic Principal Bundles Over Elliptic Curves II: The Parabolic Construction
Algebraic Geometry
2007-05-23 v2 High Energy Physics - Theory
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.
Cite
@article{arxiv.math/0006174,
title = {Holomorphic Principal Bundles Over Elliptic Curves II: The Parabolic Construction},
author = {Robert Friedman and John W. Morgan},
journal= {arXiv preprint arXiv:math/0006174},
year = {2007}
}
Comments
LaTeX, 63 pages, new section 4.6, several minor changes