Hardcover ISBN:  9780821840559 
Product Code:  CHEL/355.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470430313 
Product Code:  CHEL/355.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9780821840559 
eBook: ISBN:  9781470430313 
Product Code:  CHEL/355.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 
Hardcover ISBN:  9780821840559 
Product Code:  CHEL/355.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470430313 
Product Code:  CHEL/355.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9780821840559 
eBook ISBN:  9781470430313 
Product Code:  CHEL/355.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 

Book DetailsAMS Chelsea PublishingVolume: 355; 1971; 194 ppMSC: Primary 32
The main purpose of this book is to give an introduction to the KodairaSpencer 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.
ReadershipGraduate students and research mathematicians interested in abstract complex manifolds.

Table of Contents

Chapters

Chapter 1. Definitions and examples of complex manifolds

Chapter 2. Sheaves and cohomology

Chapter 3. Geometry of complex manifolds

Chapter 4. Applications of elliptic partial differential equations to deformations


Additional Material

Reviews

This book, a revision and organization of lectures given by Kodaira at Stanford University in 1965–66, is an excellent, wellwritten 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 selfcontained, 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


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The main purpose of this book is to give an introduction to the KodairaSpencer 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.
Graduate students and research mathematicians interested in abstract complex manifolds.

Chapters

Chapter 1. Definitions and examples of complex manifolds

Chapter 2. Sheaves and cohomology

Chapter 3. Geometry of complex manifolds

Chapter 4. Applications of elliptic partial differential equations to deformations

This book, a revision and organization of lectures given by Kodaira at Stanford University in 1965–66, is an excellent, wellwritten 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 selfcontained, 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