TY - JOUR AB - 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 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. AU - Hausel, Tamás AU - Hitchin, Nigel ID - 10704 JF - Inventiones Mathematicae SN - 0020-9910 TI - Very stable Higgs bundles, equivariant multiplicity and mirror symmetry VL - 228 ER -