18.117 | Spring 2005 | Graduate

Topics in Several Complex Variables


Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session


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.

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.


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

Course Info

As Taught In
Spring 2005
Learning Resource Types
Lecture Notes
Problem Sets