**AMS Chelsea Publishing**

Volume: 355;
1971;
194 pp;
Hardcover

MSC: Primary 32;

Print ISBN: 978-0-8218-4055-9

Product Code: CHEL/355.H

List Price: $32.00

Individual Member Price: $28.80

**Electronic ISBN: 978-1-4704-3031-3
Product Code: CHEL/355.H.E**

List Price: $32.00

Individual Member Price: $28.80

#### Supplemental Materials

# Complex Manifolds

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*James Morrow; Kunihiko Kodaira*

The main purpose of this book is to give an introduction
to the Kodaira-Spencer theory of deformations of complex structures. The
original proof of the Kodaira embedding theorem is given showing that the
restricted class of Kähler manifolds called Hodge manifolds is algebraic.
Included are the semicontinuity theorems and the local completeness theorem of
Kuranishi.

The book is based on notes taken by James Morrow from lectures given by
Kunihiko Kodaira at Stanford University in 1965–1966. Complete references
are given for the results that are used from elliptic partial differential
equations.

#### Table of Contents

# Table of Contents

## Complex Manifolds

- Cover Cover11
- Title page iii4
- Preface v6
- Contents vii8
- Complex manifolds ix10
- Definitions and examples of complex manifolds 112
- Sheaves and cohomology 2738
- Geometry of complex manifolds 8394
- Applications of elliptic partial differential equations to deformations 147158
- Bibliography 186197
- Index 189200
- Errata 193204
- Back Cover Back Cover1210

#### Readership

Graduate students and research mathematicians interested in abstract complex manifolds.

#### Reviews

This book, a revision and organization of lectures given by Kodaira at Stanford University in 1965–66, is an excellent, well-written introduction to the study of abstract complex (analytic) manifolds—a subject that began in the late 1940's and early 1950's. It is largely self-contained, except for some standard results about elliptic partial differential equations, for which complete references are given.

-- D. C. Spencer, MathSciNet

The book under review is the faithful reprint of the original edition of one of the most influential textbooks in modern complex analysis and geometry. The classic "Complex Manifolds" by J. Morrow and K. Kodaira was first published in 1971 ..., essentially as a revised and elaborated version of a set of notes taken from lectures of Fields medallist Kunihiko Kodaira at Stanford University in 1965–1966, and has maintained its role as a standard introduction to the geometry of complex manifolds and their deformations ever since.

-- Werner Kleinert, Zentralblatt MATH

Of course everyone knows Abel's exhortation that we should seek out "the masters, not their pupils," if we are to learn mathematics well and effectively. ... There is no question that this beautifully constructed book, full of elegant (and very economical) arguments underscores Abel's aforementioned dictum. Perhaps especially today, when so much is asked of the student of this material in the way of prerequisites, one can do no better than to turn to a master.

-- MAA Reviews