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32: Several complex variables and analytic spaces


Several complex variables is, naturally, the study of (differentiable) functions of more than one complex variable. The rigid constraints imposed by complex differentiability imply that, at least locally, these functions behave almost like polynomials. In particular, study of the related spaces tends to resemble algebraic geometry, except that tools of analysis are used in addition to algebraic constructs. Differential equations on these spaces and automorphisms of them provide useful connections with these other areas.


Applications and related fields

For infinite-dimensional holomorphy, See also 46G20, 58B12 [Schematic of subareas and related areas]


Note that several new secondary classifications were added in 2000.

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

Krantz, Steven G.: "What is several complex variables?", Amer. Math. Monthly 94 (1987), no. 3, 236--256. MR88e:32001

Hill, C. Denson: "What is the notion of a complex manifold with a smooth boundary?", Algebraic analysis, Vol. I, 185--201, Academic Press, Boston, MA, 1988. MR90e:32009

"Reviews in Complex Analysis 1980-1986" (four volumes), American Mathematical Society, Providence, RI, 1989. 3064 pp., ISBN 0-8218-0127-9: Reviews reprinted from Mathematical Reviews published during 1980--1986.

Fornæss, John Erik; Stensønes, Berit: "Lectures on counterexamples in several complex variables", Princeton University Press, Princeton, 1987, ISBN 0-691-08456-4

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