A Universal Family of Deformations for the Uniformising Higgs bundle
Algebraic Geometry
2011-11-29 v1 Differential Geometry
Abstract
Fix a simple complex Lie group G and a principal sl(2,C) subalgebra of Lie(G). Then the moduli space of semi-stable, topologically trivial G-Higgs bundles on a hyperbolic, spin Riemann surface acquires a marked point. This is the unique C*-fixed point on the Hitchin section. We describe a universal analytic family of deformations which provides holomorphic Darboux coordinates in a neighbourhood of the section. This is a special case of a more general deformation-theoretic construction in the spirit of Kuranishi theory. As a toy example of the latter we consider the tautological family of centralisers over the Kostant slice.
Keywords
Cite
@article{arxiv.1111.6457,
title = {A Universal Family of Deformations for the Uniformising Higgs bundle},
author = {Peter Dalakov},
journal= {arXiv preprint arXiv:1111.6457},
year = {2011}
}
Comments
Preliminary version. Comments welcome!