Seminar in KIAS

August 2018, Seoul

Title:Birational geometry of rationally connected varieties.

Abstract:The talk is about the problem of classification of algebraic varieties. Rationally connected varieties are the most understood of the classes of algebraic varieties. In dimension 2 the classification is known but already in dimension three there are many problems to overcome: more cases and singularities. I will remind of the basic notions of the minimal model program and of some results on classification in dimension 2 and 3. Then I will introduce the notion of birational rigidity and of the good model and discuss strategy of dealing with the difficulties of dimension 3.