Math 643, Fall 2019
Instructor: Jingjun
Han
Office: Krieger 221
Office Hours: W 3 PM-5 PM in
Krieger 221
Email:
jhan@math.jhu.edu
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.