2. Instructor Information
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Name |
Kim Kang-Tae |
Department |
Dept. of Mathematics |
| Email address |
kimkt@postech.ac.kr
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Homepage |
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| Office |
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Office Phone |
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| Office Hours |
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3. Course Objectives
The goal is to learn the theory of Complex Manifolds. In particular, we aim at the cohomology vanishing theorem and the embedding theorem by K. Kodaira which was one of his main contributions cited in his Fields medal award. The theories and the related techniques became the standard for the study of complex manifolds.
4. Prerequisites & require
The students should be familiar with Differentiable manifolds, Connections, Curvatures (Riemannian geometry), De Rham coholomogy. Basic knowledge of Hodge theory and system of simultaneous partial differential equations. Also some knowledge of Functional Analysis will help.
5. Grading
There will be homework assignments. But most important will be the term paper that summarizes large part of the semester's lectures.
6. Course Materials
| Title |
Author |
Publisher |
Publication
Year/Edition |
ISBN |
7. Course References
Griffiths and Harris: Principles of Algebraic Geometry, Wiley and Sons. (2014)
J.-P. Demailly, Complex analytic and differential geometry (Freely distributed PDF) 2007.
Bo Berndtsson, Lecture Notes, CTH Chalmers.se, 1995.
8. Course Plan
Weeks 1-4: Complex manifolds, Tangent and cotangent bundles, Vector bundles, Line bundles,
Sections, Connections, Curvature
Weeks 5-10: Dolbeault cohomology, d-bar equations, Solvability, (No lectures in the 8th week).
Weeks 11-12: Sheaf cohomology, Extension.
Weeks 13-15: Kodaira's vanishing and embedding theorems.
10. How to Teach & Remark
11. Supports for Students with a Disability
- Taking Course: interpreting services (for hearing impairment), Mobility and preferential seating assistances (for developmental disability), Note taking(for all kinds of disabilities) and etc.
- Taking Exam: Extended exam period (for all kinds of disabilities, if needed), Magnified exam papers (for sight disability), and etc.
- Please contact Center for Students with Disabilities (279-2434) for additional assistance