We will study the basics of the Minimal Model Program, which gives a rough birational classification of higher-dimensional algebraic varieties: singularities of varieties and pairs, cone theorem, contractions of extremal rays, Mori fiber spaces, flips and flops. The participants are expected to be familiar with the main notions of algebraic geometry, as well as with the main facts concerning the geometry of curves and surfaces.

The seminar will follow the book «Introduction to the Mori program» by Kenji Matsuki.

1.  Contraction of a $(-1)$-curve on a surface. Minimal Model Program in dimension $2$. Birational classification of surfaces.
2.  Terminal, canonical, log-terminal, and log-canonical singularities. Singularities of pairs.
3.  Vanishing theorems.
4.  Base point freeness theorem.
5.  Cone theorem.
6.  Contraction theorem.
7.  Flips and flops.
8.  Minimal models.
9.  Mori fiber spaces. Sarkisov program.

Seminar organizers
Orlov Dmitri Olegovich
Prokhorov Yuri Gennadievich
Shramov Constantin Aleksandrovich

Financial support
The seminar is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, agreement no.  075-15-2022-265).

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center