多复变量 内容简介

The third chapter presents the Weierstrass formula and the Weierstrasspreparation theorem with applications to the ring of convergent powerseries. It is shown that this ring is a factorization, a Noetherian， and a Henselring. Furthermore we indicate how the obtained algebraic theorems can beapplied to the local investigation of analytic sets. One achieves deep resultsin this connection by using sheaf theory， the basic concepts of which arediscussed in the fourth chapter. In Chapter V we introduce complex manifoldsand give several examples. We also examine the different closures of C andthe effects of modifications on complex manifolds.

多复变量 本书特色

《多复变量》:sheaf and cohomology theory, andthe real methods which stem from elliptic partial differential equations.

多复变量 目录

chapter ⅰholomorphic functions
1power series
2complex differentiable functions
3the cauchy integral
4identity theorems
5expansion in reinhardt domains
6real and complex differentiability
7holomorphic mappings
chapter ⅱdomains of holomorphy
1the continuity theorem
2pseudoconvexity
3holomorphic convexity
4the thullen theorem
5holomorphically convex domains:
6examples
7riemann domains over cn
8holomorphic hulls
chapter ⅲthe weierstrass preparation theorem
1the algebra of power series
2the weierstrass formula
3convergent power series
4prime factorization
5further consequences (hensel rings, noetherian rings)
6analytic sets
chapter ⅳsheaf theory
1sheaves of sets
2sheaves with algebraic structure
3analytic sheaf morphisms
4coherent sheaves
chapter ⅴcomplex manifolds
1complex ringed spaces
2function theory on complex manifolds
3examples of complex manifolds
4closures of cn
chapter ⅵcohomology theory
1flabby cohomology
2the cech cohomology
3double complexes
4 the cohomology sequence
5main theorem on stein manifolds
chapter ⅶreal methods
1tangential vectors
2differential forms on complex manifolds
3cauchy integrals
4dolbeault's lemma
5fine sheaves (theorems of dolbeault and de rham)
list of symbols
bibliography
index

多复变量 节选

《多复变量》:sheaf and cohomology theory, andthe real methods which stem from elliptic partial differential equations.