Valeria Bertini (Universita degli Studi di Milano) : Quotients of Hyperkähler manifolds

Abstract: Hyperkähler manifolds have been intensively studied from the 80s on, being building blocks of compact Kähler manifolds with trivial first Chern class; despite their natural role, finding examples of Hyperkähler manifolds is well known to be extremely challenging. In recent years, the focus has turned on their singular analogue, appearing naturally from the birational geometry perspective, and finally giving many new families of examples. A successful technique to produce singular examples is to consider (terminalizations of) quotients of smooth Hyperkähler manifolds. In this talk I will start presenting some recent results on singular Hyperkähler varieties constructed as quotients, and then I will turn to the case the quotient is a Calabi-Yau variety. The first part is a joint work with Grossi, Mauri and Mazzon, and the second one is work in progress with Garbagnati.