Inhaltsverzeichnis
1. Complex Spaces. - § 1. The Notion of a Complex Space. - § 2. General Properties of Complex Spaces. - § 3. Direct Products and Graphs. - § 4. Complex Spaces and Cohomology. - 2. Local Weierstrass Theory. - § 1. The Weierstrass Theorems. - § 2. Algebraic Structure of $${O_{{C^n}, 0}}$$. - § 3. Finite Maps. - §4. The Weierstrass Isomorphism. - § 5. Coherence of Structure Sheaves. - 3. Finite Holomorphic Maps. - § 1. Finite Mapping Theorem. - § 2. Rückert Nullstellensatz for Coherent Sheaves. - § 3. Finite Open Holomorphic Maps. - § 4. Local Description of Complex Subspaces in ? n. - 4. Analytic Sets. Coherence of Ideal Sheaves. - § 1. Analytic Sets and their Ideal Sheaves. - § 2. Coherence of the Sheaves i (A). - § 3. Applications of the Fundamental Theorem and of the Nullstellensatz. - § 4. Coherent and Locally Free Sheaves. - 5. Dimension Theory. - § 1. Analytic and Algebraic Dimension. - § 2. Active Germs and the Active Lemma. - § 3. Applications of the Active Lemma. - § 4. Dimension and Finite Maps. Pure Dimensional Spaces. - § 5. Maximum Principle. - § 6. Noether Lemma for Coherent Analytic Sheaves. - 6. Analyticity of the Singular Locus. Normalization of the Structure Sheaf. - § 1. Embedding Dimension. - § 2. Smooth Points and the Singular Locus. - § 3. The Sheaf M of Germs of Meromorphic Functions. - § 4. The Normalization Sheaf $${\hat O_X}$$. - § 5. Criterion of Normality. Theorem of Oka. - 7. Riemann Extension Theorem and Analytic Coverings. - § 1. Riemann Extension Theorem on Complex Manifolds. - § 2. Analytic Coverings. - § 3. Theorem of Primitive Element. - § 4. Applications of the Theorem of Primitive Element. - § 5. Analytically Normal Vector Bundles. - 8. Normalization of Complex Spaces. - § 1. One-Sheeted Analytic Coverings. - § 2. The Local ExistenceTheorem. Coherence of the Normalization Sheaf. - § 3. The Global Existence Theorem. Existence of Normalization Spaces. - § 4. Properties of the Normalization. - 9. Irreducibility and Connectivity. Extension of Analytic Sets. - § 1. Irreducible Complex Spaces. - § 2. Global Decomposition of Complex Spaces. - § 3. Local and Arcwise Connectedness of Complex Spaces. - § 4. Removable Singularities of Analytic Sets. - § 5. Theorems of Chow, Levi and Hurwitz-Weierstrass. - 10. Direct Image Theorem. - § 1. Polydisc Modules. - § 2. Proof of Lemmata F(q) and Z(q). - § 3. Sheaves of Polydisc Modules. - § 4. Coherence of Direct Image Sheaves. - § 5. Regular Families of Compact Complex Manifolds. - § 6. Stein Factorization and Applications. - Annex. Theory of Sheaves. Notion of Coherence. - §0. Sheaves. - 1. Sheaves and Morphisms 2. Restrictions, Subsheaves and Sums of Sheaves 3. Sections. Hausdorff Sheaves. - § 1. Construction of Sheaves from Presheaves. - 1. Presheaves 2. The Sheaf Associated to a Preshaf 3. Canonical Presheaves 4. Image Sheaves. - § 2. Sheaves and Presheaves with Algebraic Structure. - 1. Sheaves of Groups, Rings and A-Modules 2. The Category of A-Modules. Quotient Sheaves 3. Presheaves with Algebraic Structure 4. The Functor Hom 5. The Functor ? . - § 3. Coherent Sheaves. - 1. Sheaves of Finite Type 2. Sheaves of Relation Finite Type 3. Coherent Sheaves. - § 4. Yoga of Coherent Sheaves. - 1. Three Lemma 2. Consequences of the Three Lemma 3. Coherence of Trivial Extensions 4. Coherence of the Functors Hom and ? 5. Annihilator Sheaves. - Index of Names.
