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.
作者簡(jiǎn)介
暫缺《多復(fù)變量》作者簡(jiǎn)介
圖書(shū)目錄
Chapter Ⅰ Holomorphic Functions 1 Power Series 2 Complex Differentiable Functions 3 The Cauchy Integral 4 Identity Theorems 5 Expansion in Reinhardt Domains 6 Real and Complex Differentiability 7 Holomorphic Mappings Chapter Ⅱ Domains of Holomorphy 1 The Continuity Theorem 2 Pseudoconvexity 3 Holomorphic Convexity 4 The Thullen Theorem 5 Holomorphically Convex Domains: 6 Examples 7 Riemann Domains over Cn 8 Holomorphic Hulls Chapter Ⅲ The Weierstrass Preparation Theorem 1 The Algebra of Power Series 2 The Weierstrass Formula 3 Convergent Power Series 4 Prime Factorization 5 Further Consequences (Hensel Rings, Noetherian Rings) 6 Analytic Sets Chapter Ⅳ Sheaf Theory 1 Sheaves of Sets 2 Sheaves with Algebraic Structure 3 Analytic Sheaf Morphisms 4 Coherent Sheaves Chapter Ⅴ Complex Manifolds 1 Complex Ringed Spaces 2 Function Theory on Complex Manifolds 3 Examples of Complex Manifolds 4 Closures of Cn Chapter Ⅵ Cohomology Theory 1 Flabby Cohomology 2 The Cech Cohomology 3 Double Complexes 4 The Cohomology Sequence 5 Main Theorem on Stein Manifolds Chapter Ⅶ Real Methods 1 Tangential Vectors 2 Differential Forms on Complex Manifolds 3 Cauchy Integrals 4 Dolbeault's Lemma 5 Fine Sheaves (Theorems of Dolbeault and de Rham) List of symbols Bibliography Index
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