Complex analysis in several variables II


The purpose of this course is to study  the theory of analytic sets, proper holomorphic mappings in several  complex variables and proper holomorphic correspondences.


Description :  Proper holomorphic mappings, Alexander’s theorem, Application of the scaling technic for studying proper holomorphic mappings between strongly pseudoconvex domains (Pinchuk’s theorem). Analytic sets, local representation of analytic sets, Analytic covers, holomorphic correspondences, Normal families of proper holomorphic correspondences. Generalization of  Cartan’s theorem.

Prerequiste: M-585  M-683 and M-685 .

Grading : A Mid-term exam : 25%, Homework : 25%, Final exam: 50%.

Text-book : 1- E. Chirka  : Analytic sets (Kluwer).

2- W. Rudin, Function theory In the unit ball in C^n. Springer Verlag (1980).


 Partiel-Exam 2008