Coherent Analytic Sheaves [Paperback]

1. Complex Spaces.- ? 1. The Notion of a Complex Space.- 0. Ringed Spaces  1. The Space (?n, (O)  2. Zero Sets and Complex Model Spaces  3. Sheaves of Local ?-Algebras. ?-ringed Spaces  4. Morphisms of ?-ringed Spaces  5. Complex Spaces  6. Sections and Functions  7. Construction of Complex Spaces by Gluing  8. The Complex Projective Space ?n  9. Historical Notes.- ? 2. General Properties of Complex Spaces.- 1. Zero Sets of Ideal Sheaves  2. Closed Complex Subspaces  3. Factorization of Holomorphic Maps  4. Complex Spaces and Coherent Analytic Sheaves. Extension Principle  5. Analytic Image Sheaves  6. Analytic Inverse Image Sheaves  7. Holomorphic Embeddings.- ? 3. Direct Products and Graphs.- 1. The Bijection ?ol(X, ?n)?O(X)n. Extension of Holomorphic Maps  2. Complex Direct Products  3. Existence of Canonical Products. Local Case  4. Existence of Canonical Products. Global Case  5. Graph Space of a Holomorphic Map.- ? 4. Complex Spaces and Cohomology.- 1. Divisors  2. Holomorphic Vector Bundles  3. Line Bundles and Divisors  4. Holomorphically Convex Spaces and Stein Spaces  5. ?ech Cohomology of Analytic Sheaves  6. Cohomology of Coherent Sheaves with Respect to Stein Coverings  7. Higher Dimensional Direct Images.- 2. Local Weierstrass Theory.- ? 1. The Weierstrass Theorems.- 0. Generalities  1. The WeierstraB Division Theorem  2. The Weierstra? Preparation Theorem  3. A Simple Observation.- ? 2. Algebraic Structure of $${O_$$.- 1. Noether Property and Factoriality  2. Hensels Lemma  3. Closedness of Sub-modules.- ? 3. Finite Maps.- 1. Closed Maps  2. Finite Maps. Local Description  3. Local Representation of Image Sheaves  4. Exactness of the Functor f* for Finite Maps  5. Weierstra? Maps.- ?4. The Weierstrass Isomorphism.- 1. The Generalized Weierstra? Division Theorem  2. The Weierstra? Isomorphism  3. A Coherence Lemma  4. A Further Generalization of the Generalized Weierstra? Division Theorem.- ? 5. Coherencel³ƒ