Lectures on
Complex Differential Geometry

I. Introduction

Professor Ngaiming Mok
The University of Hong Kong

Abstract

The purposes of the lectures are two-fold: to give some basics on Complex Differential Geometry, notably on compact Kähler manifolds and on Hermitian holomorphic line bundles, and to introduce topics in Complex Differential Geometry revolving around various rigidity phenomena, presenting at the same time some open problems.

The first series of lectures will be an introduction to Complex Differential Geometry. Starting with compact Riemann surfaces, we will consider various methods for constructing meromorphic functions and projective embeddings, notably elliptic functions, sigma functions, and Poincaré series, to provide first examples of positive holomorphic line bundles. Kähler manifolds and higher-dimensional examples of compact Kähler manifolds with accompanying positive holomorphic line bundles will then be introduced, including polarized Abelian varieties and compact quotients of bounded domains together with their accompanying Bergman metrics. For the latter we will examine in particular examples of bounded symmetric domains.

Lecture 1:	January 9, 2003 (Thursday)	4:00 - 5:30pm
Lecture 2:	January 16, 2003 (Thursday)	4:00 - 5:30pm
Lecture 3:	January 23, 2003 (Thursday)	4:00 - 5:30pm
Lecture 4:	February 13, 2003 (Thursday)	4:00 - 5:30pm
Lecture 5:	February 27, 2003 (Thursday)	4:00 - 5:30pm
Lecture 6:	March 6, 2003 (Thursday)	4:00 - 5:30pm

Further Lectures: to be announced.
Lectures will be held in Room 517, Meng Wah Complex

All are welcome