@article{10704, 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 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.}, author = {Hausel, Tamás and Hitchin, Nigel}, issn = {1432-1297}, journal = {Inventiones Mathematicae}, pages = {893--989}, publisher = {Springer Nature}, title = {{Very stable Higgs bundles, equivariant multiplicity and mirror symmetry}}, doi = {10.1007/s00222-021-01093-7}, volume = {228}, year = {2022}, }