Vincent Koziarz, Université de Nancy, France

The Toledo invariant on smooth varieties of general type

Abstract

The Toledo invariant was originally defined for representations of cocompact lattices of SU(m, 1) in SU(n, 1). First, I will explain how to extend the definition of this invariant to representations of fundamental groups of smooth varieties of general type in SU(n, 1). Then, I will prove that the invariant is bounded by the volume of the canonical bundle of the variety and that if equality is achieved, the canonical model of the variety is smooth and uniformized by the complex unit ball. This is a joint work with Julien Maubon.