# Holomorphic principal bundles over elliptic curves

@article{Friedman1998HolomorphicPB, title={Holomorphic principal bundles over elliptic curves}, author={Robert Friedman and John W. Morgan}, journal={arXiv: Algebraic Geometry}, year={1998} }

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.

## 64 Citations

Holomorphic Principal Bundles Over Elliptic Curves II: The Parabolic Construction

- Mathematics, Physics
- 2000

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 characterization of holomorphic unstable principal bundles over an elliptic curve I

- Mathematics
- 2016

Let G be a connected and simply-connected simple Lie group over C and g be its Lie algebra. In this article, we establish a correspondence between the spaceC(g) of @-connections on a principal…

HIGGS BUNDLES OVER ELLIPTIC CURVES FOR COMPLEX REDUCTIVE GROUPS

- MathematicsGlasgow Mathematical Journal
- 2018

Abstract We study Higgs bundles over an elliptic curve with complex reductive structure group, describing the (normalisation of) its moduli spaces and the associated Hitchin fibration. The case of…

Poisson Geometry of Parabolic Bundles on Elliptic Curves

- 2006

The moduli space of G-bundles on an elliptic curve with additional flag structure admits a Poisson structure. The bivector can be defined using double loop group, loop group and sheaf cohomology…

POISSON GEOMETRY OF PARABOLIC BUNDLES ON ELLIPTIC CURVES

- Mathematics
- 2006

The moduli space of G-bundles on an elliptic curve with additional flag structure admits a Poisson structure. The bivector can be defined using double loop group, loop group and sheaf cohomology…

Vector Bundles and Torsion Free Sheaves on Degenerations of Elliptic Curves

- Mathematics
- 2006

In this paper we give a survey about the classification of vector bundles and torsion free sheaves on degenerations of elliptic curves. Coherent sheaves on singular curves of arithmetic genus one can…

Conjugacy Classes in Kac-Moody Groups and Principal G-Bundles over Elliptic Curves

- Mathematics
- 2006

For a simple complex Lie group G the connected components of the moduli space of G-bundles over an elliptic curve are weighted projective spaces. In this note we will provide a new proof of this…

Revisiting the moduli space of semistable G-bundles over elliptic curves

- Mathematics
- 2017

We show that the moduli space of semistable G-bundles on an elliptic curve for a reductive group G is isomorphic to a power of the elliptic curve modulo a certain Weyl group which depend on the…

Homogeneous bundles over abelian varieties

- Mathematics
- 2011

We obtain characterizations and structure results for homogeneous principal bundles over abelian varieties, that generalize work of Miyanishi and Mukai on homogeneous vector bundles. For this, we…

Higgs bundles over elliptic curves for real groups

- MathematicsThe Quarterly Journal of Mathematics
- 2019

We study topologically trivial $G$-Higgs bundles over an elliptic curve $X$ when the structure group $G$ is a connected real form of a complex semisimple Lie group $G^{\mathbb{C}}$. We achieve a…

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