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arXiv · 2101.08583

Very stable Higgs bundles, equivariant multiplicity and mirror symmetry

Tamas Hausel·Nigel Hitchin
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Abstract

We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. The main ingredients are the Bialynicki-Birula theory of ${\mathbb C}^*$-actions on semiprojective varieties, ${\mathbb C}^*$ characters of indices of ${\mathbb C}^*$-equivariant coherent sheaves, Hecke transformation for Higgs bundles, relative Fourier-Mukai transform along the Hitchin fibration, hyperholomorphic structures on universal bundles and cominuscule Higgs bundles.

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Tamas Hausel, Nigel Hitchin. 2021-01-21. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. https://doi.org/10.1007/s00222-021-01093-7

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