2024 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry D
- Academic unit or major
- Graduate major in 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
- MTH.B404
- 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 [MTH.B403 : Advanced topics 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)
None required
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
Evaluation will be based on homework. Details will be provided during class sessions.
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.C301 ： Complex Analysis I
- MTH.C302 ： Complex Analysis II
- MTH.B407 ： Advanced topics in Geometry C1
Prerequisites
Students are expected to have passed [Advanced topics in Geometry C]
Other
Lecture announcements will be posted on T2SCHOLA.