What are the necessary and sufficient conditions for a compact complex manifold to be embedded in a complex projective space? The final goal of this lecture is to explain one of the answers to this question, Kodaira's embedding theorem.
This course is a continuation of [Advanced courses in Geometry C].
Study basic knowledge of complex manifolds, especially Kähler manifolds.
Chern classes, Kahler manifolds, harmonic integrals, Kodaira's vanishing theorem, Kodaira's embedding theorem
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course
Course schedule | Required learning | |
---|---|---|
Class 1 | Chern classes | Details will be provided during each class session |
Class 2 | Kahler manifolds I | Details will be provided during each class session |
Class 3 | Kahler manifolds II | Details will be provided during each class session |
Class 4 | Harmonic integrals I | Details will be provided during each class session |
Class 5 | Harmonic integrals II | Details will be provided during each class session |
Class 6 | Kodaira's vanishing theorem | Details will be provided during each class session |
Class 7 | Kodaira's embedding theorem | Details will be provided during each class session |
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
No textbook is set.
Lecture note will be provided.
1.小林昭七,複素幾何,岩波書店
2.Raymond O. Wells, Differential Analysis on Complex Manifolds, Springer
Assignments (100%).
Students are expected to have passed [Advanced courses in Geometry C]
Lecture announcements will be posted on T2SCHOLA.