Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 32: Several complex variables and analytic spaces Introduction 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. History Applications and related fields For infinite-dimensional holomorphy, See also 46G20, 58B12 Subfields - Holomorphic functions of several complex variables
- Local analytic geometry, see also 13-XX and 14-XX
- [General theory of] Analytic spaces
- Analytic continuation
- Holomorphic convexity
- Geometric convexity [new in 2000]
- Deformations of analytic structures
- Holomorphic mappings and correspondences
- Compact analytic spaces, For Riemann surfaces, see 14HXX, 30FXX; for algebraic theory, See 14JXX
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