Topics in Several Complex Variables

Syllabus

Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Texts

Hormander, L. An Introduction to Complex Analysis in Several Variables. 2nd revised ed. Vol. 7, North-Holland Mathematical Library. Amsterdam-London: North-Holland Publishing Co. ; New York, NY: American Elsevier Publishing Co., Inc., 1973. ISBN: 0444105239.

Griffiths, P., and J. Harris. Principles of Algebraic Geometry. New York, NY: John Wiley and Sons, 1978. ISBN: 0471327921.

Supplementary Notes on Elliptic Operators.

Prerequisites

The prerequisites for this class are Functions of a Complex Variable (18.112) and Geometry of Manifolds (18.965).

Homework

There are four graded homework assignments.

Exams

There are no exams.

Topics Covered

There are five segments in this course, each involving about 6 to 8 lectures.

1. Complex variable theory on open subsets of Cⁿ. Hartog, simply pseudoconvex domains, inhomogeneous C. R.
2. Theory of complex manifolds, Kaehler manifolds.
3. Basic theorems about elliptic operators, pseudo-differential operators.
4. Hodge Theory on Kaehler manifolds.
5. Geometry Invariant Theory.

Grading

The grade for this class is based on the four homework assignments.