A surface of general type is a compact complex surface whose canonical line bundle is big and nef. They are natural generalizations of algebraic curves (compact Riemann surfaces) of genus $\ge 2$. Any such a surface is algebraic. The simplest series of examples are non-singular surfaces defined by a homogeneous equation of degree $\ge 5$ in the three-dimensional projective space. However, the class of surfaces of general type is huge and far from being limited to surfaces in $\mathbb P^3$. The study of surfaces of general type is an important part of algebraic geometry. There are still a lot of white spots here.

One of the most interesting topics is the geography. The main invariants of a surface of general type are the Chern numbers $c_1^2$ and $c_2$. The geography is a description of the possible values of $(c_1^2, c_2)$. Another area of research is the description of automorphism groups. It is known that the group of all automorphisms of a surface of general type is finite and its order is bounded by a constant depending on $c_1^2$. It is very interesting to obtain an explicit estimate and to investigate surfaces that are extreme from this point of view.

The seminar will be mainly devoted to these topics. We plan to discuss various aspects of the theory of algebraic surfaces of general type: invariants, geography, topology, automorphisms, etc. Participants are required to get acquainted with the basics of algebraic geometry.

Please, address Constantin Shramov, costya.shramov@gmail.com, for Zoom data.

Financial support. The course 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).

Lecturers
Prokhorov Yuri Gennadievich
Shramov Constantin Aleksandrovich

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