Open Access
October, 2000 Holomorphic Principal Bundles Over Elliptic Curves II: The Parabolic Construction
Robert Friedman, John W. Morgan
J. Differential Geom. 56(2): 301-379 (October, 2000). DOI: 10.4310/jdg/1090347646


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.


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Robert Friedman. John W. Morgan. "Holomorphic Principal Bundles Over Elliptic Curves II: The Parabolic Construction." J. Differential Geom. 56 (2) 301 - 379, October, 2000.


Published: October, 2000
First available in Project Euclid: 20 July 2004

zbMATH: 1033.14016
MathSciNet: MR1863019
Digital Object Identifier: 10.4310/jdg/1090347646

Rights: Copyright © 2000 Lehigh University

Vol.56 • No. 2 • October, 2000
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