Critical loci for Higgs bundles
Differential Geometry
2017-12-29 v1 Algebraic Geometry
Abstract
The paper studies the locus in the rank 2 Higgs bundle moduli space corresponding to points which are critical for d of the Poisson commuting functions. These correspond to the Higgs field vanishing on a divisor of degree D. The degree D critical locus has an induced integrable system related to K(-D)-twisted Higgs bundles. Topological and differential-geometric properties of the critical loci are addressed.
Cite
@article{arxiv.1712.09928,
title = {Critical loci for Higgs bundles},
author = {Nigel Hitchin},
journal= {arXiv preprint arXiv:1712.09928},
year = {2017}
}