Very stable Higgs bundles, equivariant multiplicity and mirror symmetry

Journal article

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.Comment: 91 pages, refereed version, to appear in Inventiones Mathematica

Authors: Hausel, T; Hitchin, N

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Inventiones Mathematicae
• Volume: 228
• Issue: 2
• Pages: 893-989
• Publication date: 2022-01-21
• DOI: 10.1007/s00222-021-01093-7
• EISSN: 1432-1297
• ISSN: 0020-9910
• Language: English
• Keywords: Mirror symmetry; Mathematical analysis; Multiplicity (mathematics); Equivariant map; Pure mathematics; Fibration; Mathematics; Particle physics; Physics; Coherent sheaf; Higgs boson