Quantization of Hitchin's equations for Higgs Bundles I
Differential Geometry
2016-01-20 v1 Algebraic Geometry
Complex Variables
Abstract
We provide an algebraic framework for quantization of Hermitian metrics that are solutions of the Hitchin equation for Higgs bundles over a projective manifold. Using Geometric Invariant Theory, we introduce a notion of balanced metrics in this context. We show that balanced metrics converge at the quantum limit towards the solution of the Hitchin equation. We relate the existence of balanced metrics to the Gieseker stability of the Higgs bundle.
Keywords
Cite
@article{arxiv.1601.04960,
title = {Quantization of Hitchin's equations for Higgs Bundles I},
author = {Mario Garcia-Fernandez and Julien Keller and Julius Ross},
journal= {arXiv preprint arXiv:1601.04960},
year = {2016}
}
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22 pages