Introduction to Complex Geometry, 08 March-25 June 2021

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

meet.google.com/vmr-oome-urw

Introduction to Complex Geometry 2017

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 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.

Lectures