Very stable Higgs bundles, equivariant multiplicity and mirror symmetry

• 成果类型: Article
• 署名作者: Hausel, Tamas; Hitchin, Nigel
• 署名单位: Institute of Science & Technology - Austria; University of Oxford
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01093-7
• 发表日期: 2022
• 页码: 893-989
• 关键词: langlands duality; FUNDAMENTAL GROUP; vector-bundles; moduli space; self-duality; REPRESENTATIONS; variety

摘要

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. Themain ingredients are the Bialynicki-Birula theory of C*-actions on semiprojective varieties, C* characters of indices of 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.