The Resource From holomorphic functions to complex manifolds, Klaus Fritzsche, Hans Grauert

From holomorphic functions to complex manifolds, Klaus Fritzsche, Hans Grauert

Label
From holomorphic functions to complex manifolds
Title
From holomorphic functions to complex manifolds
Statement of responsibility
Klaus Fritzsche, Hans Grauert
Creator
Contributor
Subject
Language
eng
Summary
"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
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Fritzsche, Klaus
Illustrations
illustrations
Index
index present
LC call number
  • QA331.7
  • DP269
LC item number
  • .F75 2002
  • .M37
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1930-
http://library.link/vocab/relatedWorkOrContributorName
Grauert, Hans
http://library.link/vocab/subjectName
  • Complex manifolds
  • Holomorphic functions
  • Fonctions holomorphes
  • Variétés complexes
  • Variétés complexes
  • Fonctions holomorphes
  • Complex manifolds
  • Holomorphic functions
  • Complexe manifolds
  • Holomorfe functies
  • Holomorphe Funktion
  • Komplexe Mannigfaltigkeit
  • Holomorphe Funktion
  • Komplexe Mannigfaltigkeit
Label
From holomorphic functions to complex manifolds, Klaus Fritzsche, Hans Grauert
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. [375]-379) and indexes
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
24 cm.
Extent
xv, 392 pages
Isbn
9780387953953
Lccn
2001057673
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
  • (OCoLC)48536644
  • (OCoLC)ocm48536644
Label
From holomorphic functions to complex manifolds, Klaus Fritzsche, Hans Grauert
Publication
Bibliography note
Includes bibliographical references (p. [375]-379) and indexes
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
24 cm.
Extent
xv, 392 pages
Isbn
9780387953953
Lccn
2001057673
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
  • (OCoLC)48536644
  • (OCoLC)ocm48536644

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