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• catalog abstract ""This book is an introduction to the theory of complex manifolds. The authors' intent is to familiarize the reader with the most important branches and methods in complex analysis of several variables and to do this as simply as possible. Therefore, the abstract concepts involving sheaves, coherence, and higher-dimensional cohomology have been completely avoided. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Nevertheless, deep results can be proved, for example, the Remmert-Stein theorem for analytic sets, finiteness theorems for spaces of cross sections in holomorphic vector bundles, and the solution of the Levi problem. Each chapter is complemented by a variety of examples and exercises. The only prerequisite needed to read this book is a knowledge of real analysis and some basic facts from algebra, topology, and the theory of one complex variable. The book can be used as a first introduction to several complex variables as well as a reference for the expert."--Jacket.".
• catalog contributor b12483575.
• catalog contributor b12483576.
• catalog created "c2002.".
• catalog date "2002".
• catalog date "c2002.".
• catalog dateCopyrighted "c2002.".
• catalog description ""This book is an introduction to the theory of complex manifolds. The authors' intent is to familiarize the reader with the most important branches and methods in complex analysis of several variables and to do this as simply as possible. Therefore, the abstract concepts involving sheaves, coherence, and higher-dimensional cohomology have been completely avoided. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Nevertheless, deep results can be proved, for example, the Remmert-Stein theorem for analytic sets, finiteness theorems for spaces of cross sections in holomorphic vector bundles, and the solution of the Levi problem. Each chapter is complemented by a variety of examples and exercises. The only prerequisite needed to read this book is a knowledge of real analysis and some basic facts from algebra, topology, and the theory of one complex variable. The book can be used as a first introduction to several complex variables as well as a reference for the expert."--Jacket.".
• catalog description "I. Holomorphic Functions -- 1. Complex Geometry -- 2. Power Series -- 3. Complex Differentiable Functions -- 4. The Cauchy Integral -- 5. The Hartogs Figure -- 6. The Cauchy-Riemann Equations -- 7. Holomorphic Maps -- 8. Analytic Sets -- II. Domains of Holomorphy -- 1. The Continuity Theorem -- 2. Plurisubharmonic Functions -- 3. Pseudoconvexity -- 4. Levi Convex Boundaries -- 5. Holomorphic Convexity -- 6. Singular Functions -- 7. Examples and Applications -- 8. Riemann Domains over C[superscript n] -- 9. The Envelope of Holomorphy -- III. Analytic Sets -- 1. The Algebra of Power Series -- 2. The Preparation Theorem -- 3. Prime Factorization -- 4. Branched Coverings -- 5. Irreducible Components -- 6. Regular and Singular Points -- IV. Complex Manifolds -- 1. The Complex Structure -- 2. Complex Fiber Bundles -- 3. Cohomology -- 4. Meromorphic Functions and Divisors -- 5. Quotients and Submanifolds -- 6. Branched Riemann Domain -- 7. Modification and Toric Closures -- V. Stein Theory -- 1. Stein Manifolds -- 2. The Levi Form -- 3. Pseudoconvexity -- 4. Cuboids -- 5. Special Coverings -- 6. The Levi Problem -- VI. Kahler Manifolds -- 1. Differential Algebra -- 2. Dolbeault Theory -- 3. Kahler Metrics -- 4. The Inner Product -- 5. Hodge Decomposition -- 6. Hodge Manifolds -- 7. Applications -- VII. Boundary Behavior -- 1. Strongly Pseudoconvex Manifolds -- 2. Subelliptic Estimates -- 3. Nebenhullen -- 4. Boundary Behavior of Biholomorphic Maps.".
• catalog description "Includes bibliographical references (p. [375]-379) and indexes.".
• catalog extent "xv, 392 p. :".
• catalog identifier "0387953957 (alk. paper)".
• catalog isPartOf "Graduate texts in mathematics ; 213".
• catalog issued "2002".
• catalog issued "c2002.".
• catalog language "eng".
• catalog publisher "New York : Springer,".
• catalog subject "515/.98 21".
• catalog subject "Complex manifolds.".
• catalog subject "Holomorphic functions.".
• catalog subject "QA331.7 .F75 2002".
• catalog tableOfContents "I. Holomorphic Functions -- 1. Complex Geometry -- 2. Power Series -- 3. Complex Differentiable Functions -- 4. The Cauchy Integral -- 5. The Hartogs Figure -- 6. The Cauchy-Riemann Equations -- 7. Holomorphic Maps -- 8. Analytic Sets -- II. Domains of Holomorphy -- 1. The Continuity Theorem -- 2. Plurisubharmonic Functions -- 3. Pseudoconvexity -- 4. Levi Convex Boundaries -- 5. Holomorphic Convexity -- 6. Singular Functions -- 7. Examples and Applications -- 8. Riemann Domains over C[superscript n] -- 9. The Envelope of Holomorphy -- III. Analytic Sets -- 1. The Algebra of Power Series -- 2. The Preparation Theorem -- 3. Prime Factorization -- 4. Branched Coverings -- 5. Irreducible Components -- 6. Regular and Singular Points -- IV. Complex Manifolds -- 1. The Complex Structure -- 2. Complex Fiber Bundles -- 3. Cohomology -- 4. Meromorphic Functions and Divisors -- 5. Quotients and Submanifolds -- 6. Branched Riemann Domain -- 7. Modification and Toric Closures -- V. Stein Theory -- 1. Stein Manifolds -- 2. The Levi Form -- 3. Pseudoconvexity -- 4. Cuboids -- 5. Special Coverings -- 6. The Levi Problem -- VI. Kahler Manifolds -- 1. Differential Algebra -- 2. Dolbeault Theory -- 3. Kahler Metrics -- 4. The Inner Product -- 5. Hodge Decomposition -- 6. Hodge Manifolds -- 7. Applications -- VII. Boundary Behavior -- 1. Strongly Pseudoconvex Manifolds -- 2. Subelliptic Estimates -- 3. Nebenhullen -- 4. Boundary Behavior of Biholomorphic Maps.".
• catalog title "From holomorphic functions to complex manifolds / Klaus Fritzsche, Hans Grauert.".
• catalog type "text".