2024년도 2학기 복소다양체 (MATH622-01) 강의계획서

1. 수업정보

학수번호 MATH622 분반 01 학점 3.00
이수구분 전공선택 강좌유형 강의실 강좌 선수과목
포스테키안 핵심역량
강의시간 월, 수 / 09:30 ~ 10:45 / 수리과학관 강의실 [104호] 성적취득 구분 G

2. 강의교수 정보

김강태 이름 김강태 학과(전공) 수학과
이메일 주소 kimkt@postech.ac.kr Homepage
연구실 전화
Office Hours

3. 강의목표

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. 강의선수/수강필수사항

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. 성적평가

There will be homework assignments. But most important will be the term paper that summarizes large part of the semester's lectures.

6. 강의교재

도서명 저자명 출판사 출판년도 ISBN

7. 참고문헌 및 자료

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. 강의진도계획

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.

9. 수업운영

10. 학습법 소개 및 기타사항

11. 장애학생에 대한 학습지원 사항

- 수강 관련: 문자 통역(청각), 교과목 보조(발달), 노트필기(전 유형) 등

- 시험 관련: 시험시간 연장(필요시 전 유형), 시험지 확대 복사(시각) 등

- 기타 추가 요청사항 발생 시 장애학생지원센터(279-2434)로 요청