2024 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry C
- 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.B403
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 3Q
- 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 will be succeeded by [Advanced topics in Geometry D].
Course description and aims
Study basic knowledge of complex manifolds, especially Kähler manifolds.
Keywords
Complex manifolds, Kähler manifolds, vector bundles, sheaves, cohomology, connections
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 | Complex functions and complex differential forms | Details will be provided during each class session. |
| Class 2 | Complex manifolds | Details will be provided during each class session. |
| Class 3 | Vector bundles | Details will be provided during each class session. |
| Class 4 | Sheaves and cohomology I | Details will be provided during each class session. |
| Class 5 | Sheaves and cohomology II | Details will be provided during each class session. |
| Class 6 | Sheaves and cohomology III | Details will be provided during each class session. |
| Class 7 | Connections on vector bundles | 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.B408 ： Advanced topics in Geometry D1
Prerequisites
Students are expected to have passed [Geometry I], [Geometry II].
Other
Lecture announcements will be posted on T2SCHOLA.