Mathematical Institute



Recent Advances in the Minimal Model Program 

by Professor Yujiro Kawamata (Tokyo)

Mid May - Mid July  2006
Monday and Wednesday 16-18, SR A, Beringstrasse 4
first lecture  May 17 !!!!

Mathematical Institute
Bonn University

A preparational course will be held April 7 – April 28, 2006
by D. Huybrechts.

Monday, Tuesday, Friday 10-12, SR F, Beringstrasse 1 (first lecture April 7)
Lectures in English or German

The preparational course is meant as a warm-up. We will try to get used to the log category and some of the basic techniques.
The following is an incomplete list of notions and results that will be discussed:
1. Cartier and Weil divisors, factorial singularities
2. The canonical divisor, Gorenstein singularities
3. termincal and canonical singularities
4. The log category, log-terminal and log-canonical singularities
5. nef, big, ample
6. Taking roots of sections and line bundles
7. Vanishing theorems (Kodaira, Kawamata-Viehweg, Grauert-Riemenschneider)
8. Non-vanishing
If I find the time, notes of the course will be posted here .

J. Kollar, S. Mori: Birational Geometry of Algebraic Varieties. Cambridge
K. Matsuki: Introduction to Mori's Program. Springer
Y. Kawamata, K. Matsuda, K. Matsuki: Introduction to the minimal model problem. Adv. Stud. Pure Math. 10;
J. Kollar (ed.): Flips and abundance for algebraic threefolds, Ast\'erisque 211, 1992.