2024 Students Enrolled in or before 2015 School of Science Mathematics
Advanced courses in Geometry D
- Academic unit or major
- Mathematics
- Instructor(s)
- Satoshi Nakamura
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Mon
- Class
- -
- Course Code
- ZUA.B334
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 4Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
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].
Course description and aims
Study basic knowledge of complex manifolds, especially Kähler manifolds.
Keywords
Chern classes, Kahler manifolds, harmonic integrals, Kodaira's vanishing theorem, Kodaira's embedding theorem
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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 |
Study advice (preparation and review)
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.
Textbook(s)
No textbook is set.
Lecture note will be provided.
Reference books, course materials, etc.
１．小林昭七，複素幾何，岩波書店
２．Raymond O. Wells, Differential Analysis on Complex Manifolds, Springer
Evaluation methods and criteria
Assignments (100%).
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.C301 ： Complex Analysis I
- MTH.C302 ： Complex Analysis II
- ZUA.B333 ： Advanced courses in Geometry C
Prerequisites
Students are expected to have passed [Advanced courses in Geometry C]
Other
Lecture announcements will be posted on T2SCHOLA.