# 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