several complex variables

**Several complex variables** is a well-established common name for function theory?/analytic geometry/potential theory in several complex variables, i.e. the study of complex manifolds of finite even dimension $d \gt 2$ as well as some generalizations like complex space?s.

The study of several complex variables is qualitatively much different from the theory of functions of one complex variable: for example, natural (inextendable) domains of holomorphy are not at all what one might guess based on the one-variable case (Hartogs lemma?), and similarly for the question of when two domains are biholomorphic?. More subtle geometric conditions such as pseudoconvexity? come to the fore.

Related $n$lab entries include Oka principle, Oka manifold, Weierstrass preparation theorem.

Revised on March 22, 2014 08:25:11
by Urs Schreiber
(82.113.121.50)