A geometric approach to Hitchin components via punctual Hilbert schemes

Online: https://bbb.mpim-bonn.mpg.de/b/gae-a7y-hhd

Hitchin components are generalizations of the classical Teichmüller space. 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.