Introduction to Complex Geometry, 08 March-25 June 2021
Monday, Friday 8:30-10:00 (Rio de Janeiro's time)
I will 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: 35% Paulo Sad's exercise. 35% Project, 30% content of the course (oral or written exam)+active
participation in the course.
In the best case, your project will be a chapter in my book with your name. If I do many corrections and
improvements, it will be a chapter with your name and mine.
You are supposed to solve 50% all exercise
(those spread in my lecture notes and Paulo Sad's exercises).
The first two months of the course you invest on exercises and the next two months on the project.
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
- 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
Week 1: 08-12 March.