Introduction to Complex Geometry, March-June 2022

Monday, Wednesday 8:30-10:00 (Rio de Janeiro's time)

meet.google.com/vmr-oome-urw

I will also use the videos of the course in 2017.

Introduction to Complex Geometry 2017

You are supposed to watch the videos before participating in the online classes. In the same time during the course I am preparing short videos which explains some theorems in less than 20 minutes.

Complex Geometry in less than 20 minutes

Final grades: 20%first exam+20%Second exam 40% Exercise. 20% Project, 20% or more, active participation in the course, suggestions and corrections to the lecture notes etc.

There will be up to 8 list of exercises.
Projects: Serre duality, Birkhoff Grothendieck theorem, Solutions of all Paulo Sad's exercise, Kodaira-Spence theory (deformation of hypersurfaces). Chern classes (Bott-Tu's book), Resolution of singularities for surface singularities (Laufer's book), Hironaka's resolution of singularities, Chow theorem and Serre's GAGA principle, algebraic varieties which are Stein but not affine, Complement of a minimal set is Stein, Calabi-Yau varieties and Bogomolov-Tian-Todorov theorem, Calabi-Yau varieties are Ricci flat.
Language: Portuguese (with Persian accent). If necessary I will mix it with English.
I will use my webcam and write in front of it. For a sample, see my seminar in GADEPs.

References

Hossein Movasati A Course in Complex Geometry and Holomorphic Foliations
Robert C. Gunning and Hugo Rossi. Analytic functions of several complex variables. Prentice-Hall Inc., Englewood Cliffs, N.J., 1965.
Robert C. Gunning. Introduction to holomorphic functions of several variables. Volume I: Function theory. Volume II: Local theory. Volume III: Homological theory.

List of exercise

List 1(Deadline 01 April): Choose 12 exercise from Chapter 2, and Chapter 14, Section 2 (Paulo Sad's exercises).

List 2 :(Dedline 15April) Choose 12 exercise from Chapter 14, Section 2 and Section 3,

List 3 :(Dedline 29 April) Choose 12 exercise from Chapter 14, Section 2 and Section 3,

Lectures

Week 1: 14-16 March, Osgood's Lemma, Riemann-Cauchy relations, Weierstrass preparation theorem, the ring of local holomorphic functions is Noetherian.

Week 2: 21-23 March. Germs of analytic varieties, extension theorems, Riemann's extension theorem, Hartogs extension theorem, Dalobeault's lemma.