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Softcover ISBN:  9780821829608 
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Softcover ISBN:  9780821829608 
Product Code:  AMSIP/18.S 
List Price:  $68.00 
MAA Member Price:  $61.20 
AMS Member Price:  $54.40 
eBook ISBN:  9781470438098 
Product Code:  AMSIP/18.E 
List Price:  $63.00 
MAA Member Price:  $56.70 
AMS Member Price:  $50.40 
Softcover ISBN:  9780821829608 
eBook ISBN:  9781470438098 
Product Code:  AMSIP/18.S.B 
List Price:  $131.00 $99.50 
MAA Member Price:  $117.90 $89.55 
AMS Member Price:  $104.80 $79.60 

Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 18; 2000; 264 ppMSC: Primary 53
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study.
This book is a selfcontained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classification theory, providing readers with some concrete examples of complex manifolds. The last part is the main purpose of the book; in it, the author discusses metrics, connections, curvature, and the various roles they play in the study of complex manifolds. A significant amount of exercises are provided to enhance student comprehension and practical experience.
Titles in this series are copublished with International Press of Boston, Inc., Cambridge, MA.
ReadershipGraduate students and research mathematicians interested in differential geometry.

Table of Contents

Reimannian geometry

Part 1 introduction

Differentiable manifolds and vector bundles

Metric, connection, and curvature

The geometry of complete Riemannian manifolds

Complex manifolds

Part 2 introduction

Complex manifolds and analytic varieties

Holomorphic vector bundles, sheaves and cohomology

Compact complex surfaces

Kähler geometry

Part 3 introduction

Hermitian and Kähler metrics

Compact Kähler manifolds

Kähler geometry


Additional Material

Reviews

Considering the vast amount of material covered and part of the material once used in summer school ... the presentation is precise and lucid ... If one has some background or previous exposure to some of the material in the book, studying this book would be really enjoyable and one could learn a lot from it. It is also a very good reference book.
Mathematical Reviews


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The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study.
This book is a selfcontained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classification theory, providing readers with some concrete examples of complex manifolds. The last part is the main purpose of the book; in it, the author discusses metrics, connections, curvature, and the various roles they play in the study of complex manifolds. A significant amount of exercises are provided to enhance student comprehension and practical experience.
Titles in this series are copublished with International Press of Boston, Inc., Cambridge, MA.
Graduate students and research mathematicians interested in differential geometry.

Reimannian geometry

Part 1 introduction

Differentiable manifolds and vector bundles

Metric, connection, and curvature

The geometry of complete Riemannian manifolds

Complex manifolds

Part 2 introduction

Complex manifolds and analytic varieties

Holomorphic vector bundles, sheaves and cohomology

Compact complex surfaces

Kähler geometry

Part 3 introduction

Hermitian and Kähler metrics

Compact Kähler manifolds

Kähler geometry

Considering the vast amount of material covered and part of the material once used in summer school ... the presentation is precise and lucid ... If one has some background or previous exposure to some of the material in the book, studying this book would be really enjoyable and one could learn a lot from it. It is also a very good reference book.
Mathematical Reviews