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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Nakamura Satoshi
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- -
- Group
- -
- Course number
- MTH.B404
- Credits
- 1
- Academic year
- 2024
- Offered quarter
- 4Q
- Syllabus updated
- 2024/3/14
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
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].
Student learning outcomes
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 that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course
Course schedule/Required learning
| 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. |
Out-of-Class Study Time (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
Assessment criteria and methods
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 (i.e., required knowledge, skills, courses, etc.)
Students are expected to have passed [Advanced topics in Geometry C]
Other
Lecture announcements will be posted on T2SCHOLA.
