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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Honda Nobuhiro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri3-4(H137)
- Group
- -
- Course number
- MTH.C407
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 3Q
- Syllabus updated
- 2017/8/28
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
Basic materials on compact Kaehler manifolds will be explained.
Student learning outcomes
To understand special properties on cohomology groups on compact Kahler manifolds, as well as their proofs.
Keywords
Kahler metric, Kahler manifold, Hodge decomposition, Kahelr identity, Lefschetz decomposition, primitive cohomology, Hodge index theorem, divisors and line bundles
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard course
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Kahler manifolds and examples | Details will be provided during each class session |
| Class 2 | Hodge decomposition | |
| Class 3 | Kahler identity | |
| Class 4 | primitive cohomology | |
| Class 5 | Lefschetz decomposition | |
| Class 6 | index formula | |
| Class 7 | divisors and line bundles | |
| Class 8 | Picard groups and Chern classes |
Textbook(s)
None
Reference books, course materials, etc.
P. Griffiths, J. Harris, "Principles of Algebraic Geometry", Wiley-Interscience
R.O.Wells, Differential analysis on complex manifolds, Springer GTM 65
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.B505 ： Advanced topics in Geometry E1
- MTH.B506 ： Advanced topics in Geometry F1
Prerequisites (i.e., required knowledge, skills, courses, etc.)
none
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
honda[at]math.titech.ac.jp
