Syllabus

Amazon logo When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more.

Texts

Amazon logo 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.

Amazon logo 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.