Math 643, Fall 2019
Instructor: Jingjun Han
Office: Krieger 221
Office Hours: W 3 PM-5 PM in Krieger 221
Lectures: TTh 9:00AM - 10:15AM
References: Introduction to the Mori Program, Kenji Matsuki, Springer, 2002.
Lectures on complements on log surfaces, Yuri G. Prokhorov, MSJ Memoirs, vol. 10. 2001.
Birational Geometry of Algebraic Varieties, Janos Kollár, Shigefumi Mori, Cambridge University Press, 1998
This is an introduction course on the minimal model program. For surfaces, we will cover the cone theorem, the non-vanishing for pairs and generalized polarized pairs, the abundance theorem, Sarkisov program, Zariski decomposition, the ACC for MLD, the ACC for a-LCT, the theory of complements, Birkar-Borisov-Alexeev-Borisov, boundedness of LCT of linear systems, etc.
1.The cone theorem, Sarkisov program (Chapter 1-2, Introduction to the Mori Program)
2.The non-vanishing for pairs and the abundance theorem (Chapter 11, Flips and abundance for algebraic threefolds; ON NUMERICAL NONVANISHING FOR GENERALIZED LOG CANONICAL PAIRS, https://arxiv.org/pdf/1808.06361.pdf)
3. the ACC for MLD, the ACC for a-LCT (Valery Alexeev, Two two--dimensional terminations, Duke Math. J., 69(3), 1993: 527—545; V.V. Shokurov, A.c.c. in codimension 2, 1991 (preprint).)
4. the theory of complements, Birkar-Borisov-Alexeev-Borisov, boundedness of LCT of linear systems (Lectures on complements on log surfaces, etc.)
Grading: No homework. The final assessment for this class will be a 10-20 pages paper on a topic related to the course material.