Evento
Descrizione:
Abstract: Mori's celebrated Bend-and-Break theorem has been a fundamental tool in studying the birational geometry of varieties and curves on them. Confusingly for newcomers to the subject, there are actually several different (related) results that are all referred to as "Bend-and-Break." In this talk, we will review three common versions of Bend-and-Break, and explain how a new "Bend-and-Shatter" lemma allows us to improve the degree bound coming from one of the versions. As an application, we discuss how our new result gives the optimal bound on lengths of extremal rays.