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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.C408
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 4Q
- Syllabus updated
- 2017/9/22
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
This course is a succession of MTH.C407. Basic materials on compact Kaehler manifolds will be explained.
Student learning outcomes
Students are expected to learn
・representation of Chern classes in terms of curvature forms,
・vanishing theorem of cohomology groups under positivity condition of curvature
・computations of numerical invariants of simple algebraic varieties
Keywords
connection and curvature, Chern classes, vanishing theorem, hyperplane theorem, adjunction formula
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 | connection of complex vector bundles | Details will be provided during each class session |
| Class 2 | Chern classes of holomorphic line bundles | |
| Class 3 | geometric interpretation of Chern classes | |
| Class 4 | vanishing theorem | |
| Class 5 | application of vanishing theorem | |
| Class 6 | adjunction formula and its application | |
| Class 7 | numerical invariant of algebraic surfaces |
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.C407 ： Advanced topics in Analysis C1
- MTH.B505 ： Advanced topics in Geometry E1
- MTH.B506 ： Advanced topics in Geometry F1
Prerequisites (i.e., required knowledge, skills, courses, etc.)
none
