Several complex variables and complex manifolds. 2 / Mike Field.

Format:

Book

Author/Creator:

Field, Mike, author.

Series:

London Mathematical Society lecture note series ; 66.

London Mathematical Society lecture note series ; 66

Language:

English

Subjects (All):

Functions of several complex variables.

Complex manifolds.

Physical Description:

1 online resource (vii, 211 pages) : digital, PDF file(s).

Other Title:

Several Complex Variables & Complex Manifolds II

Place of Publication:

Cambridge : Cambridge University Press, 1982.

Language Note:

English

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.

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

Notes:

Title from publisher's bibliographic system (viewed on 31 May 2016).

Includes bibliographical references and indexes.

ISBN:

1-139-88409-3

1-107-36612-7

1-107-37085-X

1-107-36121-4

1-107-36867-7

1-299-40392-1

1-107-36366-7

0-511-62932-X