Geometric approach to Hitchin components via punctual Hilbert schemes
Apparaît dans la collection : Teichmüller Theory: Classical, Higher, Super and Quantum / Théorie de Teichmüller : classique, supérieure, super et quantique
I will describe a program to describe Hitchin components as the moduli space of some new geometric structure on the surface. This geometric structure generalizes the complex structure. Its construction uses the punctual Hilbert scheme of the plane. It should give a unified description of Hitchin components without fixed complex structure on the surface. I also present a generalization to character varieties for non split real groups in the spirit of G-Higgs bundles.
