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arXiv · 1601.04960

Quantization of Hitchin's equations for Higgs Bundles I

Mario Garcia-Fernandez·Julien Keller·Julius Ross
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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.

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BibTeXRIS

Mario Garcia-Fernandez, Julien Keller, Julius Ross. 2016-01-19. Quantization of Hitchin's equations for Higgs Bundles I. https://arxiv.org/abs/1601.04960

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