Math 936 --- Complex Manifolds          Spring 06

Prof. T. Parker
Mathematics Department
A346 Wells Hall
(517) 353-8493

Office hours:

Mondays, Wednesdays & Fridays 2:45 -- 3:45
and by appointment

parker@math.msu.edu

Goals: Differential topology is the study of the global properties of manifolds. It is an appealing subject because many fascinating facts can be uncovered and developed using only the tools of advanced calculus. The aim of this course is to explore the subject of topology without a lengthy development of algebraic machinery.

Topics will include Hermitian metrics, connections, curvature, Hodge theorem. Kaehler metrics, Kodaira vanishing theorem, Chern classes.

This is a course on complex manifolds from a geometric analysis perspective. It will cover complex tangent spaces and differential forms, hler structures, the Hodge theorem, curvature and Chern forms. It will go on to cover Lefschetz theorems, Serre Duality, the Hirzebrech-Riemann-Roch Theorem, and the Kodaira Vanishing and Kodaira Embedding Theorems.

While this course is officially a sequel to Math 935, that is not a prerequisite. Students should be familiar with manifolds, differential forms, homology and cohomology. Beyond that, the assumed background knowledge will be adjusted to the level appropriate for the students in the class.

Text:

Principles of Algebraic Geometry by P. Griffiths and J. Harris.

Other helpful reference books:

• Complex Manifolds by Daniel Huybrechts, and
• Compact Complex Surfaces by W. Barth, K. Hulek, C. Peters and A. Van de Ven
• Complex Manifolds and Deformations of Complex Structures by K. Kodaira