منفردهای پیچیده (سری آتنا؛ موضوعات منتخب در ریاضیات)

Main subject categories: • Complex manifolds • Sheaves • Cohomology • • Geometry of complex manifolds • Applications of elliptic partial differential equationsThis volume serves as an introduction to the Kodaira-Spencer theory of deformations of complex structures. Based on notes taken by James Morrow from lectures given by Kunihiko Kodaira at Stanford University in 1965-1966, the book gives the original proof of the Kodaira embedding theorem, 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. Readers are assumed to know some algebraic topology. Complete references are given for the results that are used from elliptic partial differential equations. The book is suitable for graduate students and researchers interested in abstract complex manifolds. 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 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. Cover......Page 1 Title......Page 2 Preface......Page 4 Contents......Page 6 1. Holomorphic Functions......Page 10 2. Complex Manifolds and Pseudogroup Structures......Page 16 3. Some Examples of Construction (or Description) of Compact Complex Manifolds......Page 20 4. Analytic Families; Deformations......Page 27 1. Germs of Functions......Page 36 2. Cohomology Groups......Page 39 3. Infinitesimal Deformations......Page 44 4. Exact Sequences......Page 65 5. Vector Bundles......Page 71 6. A Theorem of Dolbeault (A fine resolution of O)......Page 82 1. Hermitian Metrics; Kahler Structures......Page 92 2. Norms and Dual Forms......Page 101 3. Norms for Holomorphic Vector Bundles......Page 109 4. Applications of Results on Elliptic Operators......Page 111 5. Covariant Differentiation on Kahler Manifolds......Page 115 6. Curvatures on Kahler Manifolds......Page 125 7. Vanishing Theorems......Page 134 8. Hodge Manifolds......Page 143 1. Infinitesimal Deformations......Page 156 2. An Existence Theorem for Deformations I. (No Obstructions)......Page 164 3. An Existence Theorem for Deformations II. (Kuranishi's Theorem)......Page 174 4. Stability Theorem......Page 182 Bibliography......Page 195 Index......Page 198 Errata......Page 202

This volume serves as an introduction to the Kodaira-Spencer theory of deformations of complex structures. Based on notes taken by James Morrow from lectures given by Kunihiko Kodaira at Stanford University in 1965-1966, the book gives the original proof of the Kodaira embedding theorem, showing that the restricted class of Kahler manifolds called Hodge manifolds is algebraic. Included are the semicontinuity theorems and the local completeness theorem of Kuranishi. Readers are assumed to know some algebraic topology. Complete references are given for the results that are used from elliptic partial differential equations. The book is suitable for graduate students and researchers interested in abstract complex manifolds.

This volume serves as an introduction to the Kodaira-Spencer theory of deformations of complex structures. Based on notes taken by James Morrow from lectures given by Kunihiko Kodaira at Stanford University in 1965-1966, the book gives the original proof of the Kodaira embedding theorem, 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. Readers are assumed to know some algebraic topology. Complete references are given for the results that are used from elliptic partial differential equations. The book is suitable for graduate students and researchers interested in abstract complex manifolds. Serves as an introduction to the Kodaira-Spencer theory of deformations of complex structures. Based on lectures given by Kunihiko Kodaira at Stanford University in 1965-1966, this book gives the original proof of the Kodaira embedding theorem, showing that the restricted class of Kahler manifolds called Hodge manifolds is algebraic. [by] James Morrow [and] Kunihiko Kodaira. Bibliography: P. 186-187.