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Seminar by Yu. G. Prokhorov and С. A. Shramov "Surfaces of general type"
September 15–December 29, 2021, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom

We kindly ask all participants, including remote ones and those
watching recorded videos, to register at https://forms.gle/uGW1aohpfJ7Tbrfc7.


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.

Просьба к участникам обращаться к Константину Александровичу Шрамову, costya.shramov@gmail.com, за данными для подключения к занятиям через Zoom.


First lecture of the 2021/2022 fall semester: September 15.


Financial support. The course is supported by the Simons Foundation and the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

RSS: Forthcoming seminars

Lecturers
Prokhorov Yuri Gennadievich
Shramov Сonstantin Aleksandrovich

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


Seminar by Yu. G. Prokhorov and С. A. Shramov "Surfaces of general type", September 15–December 29, 2021

October 27, 2021 (Wed)
1. Seminar 7. Surfaces of general type
Yu. G. Prokhorov, С. A. Shramov
October 27, 2021 18:00, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom

October 20, 2021 (Wed)
2. Seminar 6. Surfaces of general type
Yu. G. Prokhorov, С. A. Shramov
October 20, 2021 18:00, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom

October 13, 2021 (Wed)
3. Seminar 5. Surfaces of general type
Yu. G. Prokhorov, С. A. Shramov
October 13, 2021 18:00, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom

October 6, 2021 (Wed)
4. Seminar 4. Surfaces of general type
Yu. G. Prokhorov, С. A. Shramov
October 6, 2021 18:00, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom

September 29, 2021 (Wed)
5. Seminar 3. Surfaces of general type
Yu. G. Prokhorov, С. A. Shramov
September 29, 2021 18:00, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom

September 22, 2021 (Wed)
6. Seminar 2. Surfaces of general type
Yu. G. Prokhorov, С. A. Shramov
September 22, 2021 18:00, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom

September 15, 2021 (Wed)
7. Seminar 1. Surfaces of general type
Yu. G. Prokhorov, С. A. Shramov
September 15, 2021 18:00, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom
 
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