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Introduction to Complex Manifolds
 
John M. Lee University of Washington, Seattle, WA
Hardcover ISBN:  978-1-4704-7695-3
Product Code:  GSM/244
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Softcover ISBN:  978-1-4704-7782-0
Product Code:  GSM/244.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7781-3
Product Code:  GSM/244.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7782-0
eBook: ISBN:  978-1-4704-7781-3
Product Code:  GSM/244.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
Click above image for expanded view
Introduction to Complex Manifolds
John M. Lee University of Washington, Seattle, WA
Hardcover ISBN:  978-1-4704-7695-3
Product Code:  GSM/244
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Softcover ISBN:  978-1-4704-7782-0
Product Code:  GSM/244.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7781-3
Product Code:  GSM/244.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7782-0
eBook ISBN:  978-1-4704-7781-3
Product Code:  GSM/244.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 2442024; 361 pp
    MSC: Primary 32; Secondary 53

    Complex manifolds are smooth manifolds endowed with coordinate charts that overlap holomorphically. They have deep and beautiful applications in many areas of mathematics. This book is an introduction to the concepts, techniques, and main results about complex manifolds (mainly compact ones), and it tells a story. Starting from familiarity with smooth manifolds and Riemannian geometry, it gradually explains what is different about complex manifolds and develops most of the main tools for working with them, using the Kodaira embedding theorem as a motivating project throughout.

    The approach and style will be familiar to readers of the author's previous graduate texts: new concepts are introduced gently, with as much intuition and motivation as possible, always relating new concepts to familiar old ones, with plenty of examples. The main prerequisite is familiarity with the basic results on topological, smooth, and Riemannian manifolds. The book is intended for graduate students and researchers in differential geometry, but it will also be appreciated by students of algebraic geometry who wish to understand the motivations, analogies, and analytic results that come from the world of differential geometry.

    Readership

    Graduate students and researchers interested in complex manifolds and differential geometry.

  • Table of Contents
     
     
    • Chapters
    • The basics
    • Complex submanifolds
    • Holomorphic vector bundles
    • The Dolbeault complex
    • Sheaves
    • Sheaf cohomology
    • Connections
    • Hermitian and Kähler manifolds
    • Hodge theory
    • The Kodaira embedding theorem
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 2442024; 361 pp
MSC: Primary 32; Secondary 53

Complex manifolds are smooth manifolds endowed with coordinate charts that overlap holomorphically. They have deep and beautiful applications in many areas of mathematics. This book is an introduction to the concepts, techniques, and main results about complex manifolds (mainly compact ones), and it tells a story. Starting from familiarity with smooth manifolds and Riemannian geometry, it gradually explains what is different about complex manifolds and develops most of the main tools for working with them, using the Kodaira embedding theorem as a motivating project throughout.

The approach and style will be familiar to readers of the author's previous graduate texts: new concepts are introduced gently, with as much intuition and motivation as possible, always relating new concepts to familiar old ones, with plenty of examples. The main prerequisite is familiarity with the basic results on topological, smooth, and Riemannian manifolds. The book is intended for graduate students and researchers in differential geometry, but it will also be appreciated by students of algebraic geometry who wish to understand the motivations, analogies, and analytic results that come from the world of differential geometry.

Readership

Graduate students and researchers interested in complex manifolds and differential geometry.

  • Chapters
  • The basics
  • Complex submanifolds
  • Holomorphic vector bundles
  • The Dolbeault complex
  • Sheaves
  • Sheaf cohomology
  • Connections
  • Hermitian and Kähler manifolds
  • Hodge theory
  • The Kodaira embedding theorem
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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