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
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 nonsingular surfaces defined by a
homogeneous equation of degree $\ge 5$ in the threedimensional 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. 0751520191614).
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 20, 2021 (Wed) 

1. 
Lecture 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) 

2. 
Lecture 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) 

3. 
Lecture 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) 

4. 
Lecture 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) 

5. 
Lecture 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) 

6. 
Lecture 1. Surfaces of general type Yu. G. Prokhorov, С. A. Shramov September 15, 2021 18:00, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom





