Families of higher dimensional varieties

János Kollár (Princeton University)

Dates:

Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Abstract:

The moduli space of smooth projective curves, and its compactification by nodal curves, turned out to be some of the most studied varieties in mathematics and string theory. The analogous theory for the moduli of higher dimensional varieties was completed recently, after 30 years of work by many mathematicians. The aim of the lectures is to outline this theory.

Lecture 1 will focus on examples that show unexpected features of the higher dimensional theory. The main definitions and theorems will be explained in lecture 2. The remaining lectures will be independent of each other, each treating a topic in moduli theory with connections to other questions in mathematics.

Lecture notes of Professor Kollar: part_1-3 part_4-6