Ana Victoria Martins Quedo (Università di Bologna)

Abstract: As a consequence of the famous Cone theorem, it is known that the nef cone of a Fano variety is rational polyhedral, which implies these varieties have finitely many birational contractions and fiber space structures, a particularly interesting property when we consider the minimal model program. But what can we say about other classes of varieties? The Kawamata-Morrison cone conjecture is an open problem that predicts the existence of a rational polyhedral domain for the action of the automorphism group on the nef cone of projective manifolds with numerically trivial canonical divisor. In this talk, I will start with a quick review on divisors and the canonical class and I will introduce the conjecture and convey an idea of the proof for the case when the manifold is the quotient of an abelian variety by a finite group, a result obtained together with Martina Monti.