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E-book
Author Field, Mike.

Title Several complex variables and complex manifolds. II / Mike Field
Published Cambridge : Cambridge University Press, 1982

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Description 1 online resource
Series London Mathematical Society Lecture Note Series ; no. 66
London Mathematical Society lecture note series ; no. 66.
Contents Cover; Title; Copyright; Preface; Contents; Chapter 5. Calculus on Complex Manifolds; Introduction.; 1. Review of Linear Algebra; 2. Calculus on Differential Manifolds; 3. Complexification; 4. Complex Linear Algebra; 5. Generalities on Complex Vector Bundles; 6. Tangent and Cotangent Bundles of a Complex Manifold; 7. Calculus on a Complex Manifold; 8. The Dolbeault-Grothendieck Lemma; 9. Holomorphic Vector Bundles on Compact Complex Manifolds; 10. Pseudoconvexivity and Stein Manifolds; Chapter 6. Sheaf Theory; Introduction; 1. Sheaves and Presheaves; 2. Envelope of Holomorphy
3. Sheaf CohomologyChapter 7. Coherent Sheaves; Introduction.; 1. Coherent Sheaves; 2. Coherent Sheaves on a Stein Manifold; 3. The Finiteness Theorem of Cartan and Serre; 4. The Finiteness Theorem of Grauert; 5. Coherent Sheaves on Protective Space; 6. The Kodaira Embedding Theorem; Bibliography; Index
Summary This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those topics and a broad introduction to the field. Part I is suitable for advanced undergraduates and beginning postgraduates whilst Part II is written more for the graduate student. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a working knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts provide an introduction to the more advanced works in the subject
Notes Title from publishers bibliographic system (viewed on 22 Dec 2011)
Bibliography Includes bibliographical references and indexes
Notes Print version record
Subject Functions of several complex variables.
Manifolds (Mathematics)
MATHEMATICS -- Complex Analysis.
Functions of several complex variables
Manifolds (Mathematics)
Form Electronic book
ISBN 9781107361218
1107361214
9780511629327
051162932X
9781139884099
1139884093