Spring 2006
Complex Algebraic Geometry
複代數幾何
Course
Information
Instructor : Jungkai Chen陳榮凱
Place: Math Bldg 103
Hours: Fri. 2,3,4
First meeting: Feb 24. 2005.
Contents：
This course is intended to
introduce some important aspects in complex geometry, including Hodge theory,
variation of Hodge structure and analytic methods in algebraic geometry.
The following is the plan:
1.
Complex manifolds
2.
Kaehler metrics
3.
Harmonic forms
4.
Hodge decomposition and Lefschetz decomposition
5.
Hodge structure and polarization
6.
Variation of Hodge structure
7.
Vanishing theorems
8.
Semipositivity
9.
Singular Hermitian metric on positive line
bundles
10. Some applications
Course
prerequisite：
Complex analysis and geometry are
required. Some experience in algebraic geometry is preferred..
Reference material
( textbook(s) )：
Voisin, Claire Hodge theory and complex algebraic geometry. I. Cambridge
Studies in Advanced Mathematics, 76.
Grading scheme：
Homework 50%
Presentation 30%
Participation 20%