Math 257 General Information
Spring, 2004
Course Description
The course will focus on the linear and non-linear methods in complex geometry.The theorems discussed will be
centered on two fundamental questions in the subject.
Namely when a compact complex manifold is a submanifold of the projective
space and how many different holomorphic structures exist on a fixed
differential (topological) structure of a given manifold.
We will start with basics on complex differential geometry.
The linear methods include the L^2 estimates, Bochner-Kodaira techniques in the application of
vanishing and embedding theorems, Hodge theory and its application in
deformation theory. The non-linear methods cover the harmonic
mapping method in the solution to Frankel conjecture, Siu's strong rigidity theorem, the construction of Kaehler-Einstein metrics via nonlinear
elliptic/parabolic PDE. The basics of calculus on manifolds and manifold
topology are assumed.
There will be no final exam.
The complete course schedule is available.
Instructors
| Name |
Office |
E-mail |
Phone |
Office Hours |
| Ni, Lei |
AP&M 5250 |
lni@math.ucsd.edu |
534-2704 |
MWF 11:00-12:00am |
|
Course Time and Location
| Section |
Instructor |
Time |
Place |
| A00 |
Ni |
MWF 11:00-11:50 am |
APM 5829 |
|
Texts
Text: (1) Differential Analysis on Complex Manifolds, R.O. Wells;
(2) Canonical Metrics in Kaehler Geometry, G. Tian
(3) Recommended Reference: Complex manifolds,
K. Kodaira and J. Morrow
Exams
There will be no exam.
Homework
There will be weekly homework
assignments. Homework should be turned by the end of the quarter.
Schedule
The course schedule is available.
Check the schedule page regularly, because it is subject to change
(especially those portions currently far in the future).
Grades
Grades will be based on the following percentages.
Last modified: Wed March 04, 14:49:08 PST 2004