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.
The prerequisites for this class are Functions of a Complex Variable (18.112) and Geometry of Manifolds (18.965).
There are four graded homework assignments.
There are no exams.
There are five segments in this course, each involving about 6 to 8 lectures.
- Complex variable theory on open subsets of Cn. Hartog, simply pseudoconvex domains, inhomogeneous C. R.
- Theory of complex manifolds, Kaehler manifolds.
- Basic theorems about elliptic operators, pseudo-differential operators.
- Hodge Theory on Kaehler manifolds.
- Geometry Invariant Theory.
The grade for this class is based on the four homework assignments.