Lectures on Complex Manifolds^*

Professor Ngaiming Mok

The University of Hong Kong

This course gives an introduction to basic notions on complex manifolds both on the algebraic and on the analytic sides. This will include sheaves, Cech cohomology, de Rham and Dolbeault cohomologies, Hermitian and Kähler manifolds, Hermitian holomorphic vector bundles, harmonic forms, vanishing theorems, Kodaira’s Embedding Theorem, and infinitesimal deformation of complex structures. Additional topics on complex manifolds, either differential-geometric or algebro-geometric in nature, will be discussed to illustrate recent progress in the subject.

References:

[GH] Griffiths, P. & Harris, J. Principles of Algebraic Geometry, Pure and Applied Mathemtics, Wiley-Interscience Publishers, New York 1978.

[K] Kodaira, K. Complex Manifolds and Deformation of Complex Structures, Grundlehren der mathematischen Wissenschaften 283, Springer-Verlag, Berlin-Heidelberg 1986.

[M] Mok, N. Metric Rigidity Theorems on Hermitian Locally Symmetric Manifolds, World Scientific, Singapore-New Jersey 1989.

Lecture 1:	February 7, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 2:	February 14, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 3:	February 21, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 4:	February 28, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 5:	March 7, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 6:	March 21, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 7:	March 28, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 8:	April 4, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 9:	April 11, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 10:	April 18, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 11:	April 25, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 12:	May 2, 2005 (Tuesday)	3:00 – 5 :45pm
Lecture 13:	May 9, 2005 (Tuesday)	3:00 – 5 :45pm

Lectures will be held in Room 517, Meng Wah Complex, HKU

* Lectures of a graduate course MATH6202 Complex Manifolds of the joint

HKU-CUHK-HKUST Centre for Advanced Study (Mathematics)

All are welcome