Deformations Of Compact Complex Manifolds

Author : K. Kodaira
Publisher : Springer Science & Business Media
ISBN 13 : 1461385903
Total Pages : 476 pages
Book Rating : 4.05/5 ( download)

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Download or read book Complex Manifolds and Deformation of Complex Structures written by K. Kodaira and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of complex manifolds and their deformations. Deformation of the complex structure of Riemann surfaces is an idea which goes back to Riemann who, in his famous memoir on Abelian functions published in 1857, calculated the number of effective parameters on which the deformation depends. Since the publication of Riemann's memoir, questions concerning the deformation of the complex structure of Riemann surfaces have never lost their interest. The deformation of algebraic surfaces seems to have been considered first by Max Noether in 1888 (M. Noether: Anzahl der Modulen einer Classe algebraischer Fliichen, Sitz. K6niglich. Preuss. Akad. der Wiss. zu Berlin, erster Halbband, 1888, pp. 123-127). However, the deformation of higher dimensional complex manifolds had been curiously neglected for 100 years. In 1957, exactly 100 years after Riemann's memoir, Frolicher and Nijenhuis published a paper in which they studied deformation of higher dimensional complex manifolds by a differential geometric method and obtained an important result. (A. Fr61icher and A. Nijenhuis: A theorem on stability of complex structures, Proc. Nat. Acad. Sci., U.S.A., 43 (1957), 239-241).

Author : Masatake Kuranishi
Publisher :
ISBN 13 :
Total Pages : 100 pages
Book Rating : 4.43/5 ( download)

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Download or read book Deformations of Compact Complex Manifolds written by Masatake Kuranishi and published by . This book was released on 1971 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : D. Sundararaman
Publisher : Pitman Publishing
ISBN 13 :
Total Pages : 278 pages
Book Rating : 4.85/5 ( download)

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Download or read book Moduli, Deformations, and Classifications of Compact Complex Manifolds written by D. Sundararaman and published by Pitman Publishing. This book was released on 1980 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : James A. Morrow
Publisher : American Mathematical Soc.
ISBN 13 : 082184055X
Total Pages : 210 pages
Book Rating : 4.59/5 ( download)

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Download or read book Complex Manifolds written by James A. Morrow and published by American Mathematical Soc.. This book was released on 2006 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Thiruvalloor E. Venkata Balaji
Publisher : Universitätsverlag Göttingen
ISBN 13 : 3941875329
Total Pages : 241 pages
Book Rating : 4.26/5 ( download)

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Download or read book An Introduction to Families, Deformations and Moduli written by Thiruvalloor E. Venkata Balaji and published by Universitätsverlag Göttingen. This book was released on 2010 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Moduli Theory is one of those areas of Mathematics that has fascinated minds from classical to modern times. This has been so because it reveals beautiful Geometry naturally hidden in questions involving classification of geometric objects and because of the profound use of the methods of several areas of Mathematics like Algebra, Number Theory, Topology and Analysis to achieve this revelation. A study of Moduli Theory would therefore give senior undergraduate and graduate students an integrated view of Mathematics. The present book is a humble introduction to some aspects of Moduli Theory.

Author : Masatake Kuranishi
Publisher : Montreal, U. P
ISBN 13 : 9780840501714
Total Pages : 99 pages
Book Rating : 4.14/5 ( download)

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Download or read book Deformations of Compact Complex Manifolds written by Masatake Kuranishi and published by Montreal, U. P. This book was released on 1971 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Kunihiko Kodaira
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.31/5 ( download)

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Download or read book Existence of Complex Structure on a Differentiable Family of Deformations of Compact Complex Manifolds written by Kunihiko Kodaira and published by . This book was released on 1958 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Steven Bell
Publisher : Springer Science & Business Media
ISBN 13 : 9783540629955
Total Pages : 324 pages
Book Rating : 4.55/5 ( download)

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Download or read book Complex Manifolds written by Steven Bell and published by Springer Science & Business Media. This book was released on 1997-12-11 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990. They are surveys, meant to facilitate access to some of the many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and many other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups, and mathematical physics being only the most obvious of these branches. Each of these articles should serve not only to describe the particular circle of ideas in complex analysis with which it deals but also as a guide to the many mathematical ideas related to its theme.

Author : Kunihiko Kodaira
Publisher :
ISBN 13 :
Total Pages : 2 pages
Book Rating : 4.97/5 ( download)

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Download or read book On Stability of Compact Submanifolds of Complex Manifolds written by Kunihiko Kodaira and published by . This book was released on 1961 with total page 2 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stability of compact submanifolds of complex manifolds and some related topics are discussed. A compact submanifold V of a complex manifold W is said to be stable if any small deformation W T OF contains a small deformation Vt of V. Let psi be the sheaf over V of germs of holomorphic sections of the normal bundle of V in W. If the first cohomology group H1(V, psi) vanishes then V is a stable submanifold of W.A fibre structure of a compact fibred complex manifold M is said to be stable if any small deformation Mt of M retains a fibre structure. If each fibre of M is regular then the fibre structure of M is stable. (Author).

Author : R. O. Wells
Publisher : Springer Science & Business Media
ISBN 13 : 147573946X
Total Pages : 269 pages
Book Rating : 4.66/5 ( download)

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Download or read book Differential Analysis on Complex Manifolds written by R. O. Wells and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. The third edition of this standard reference contains a new appendix by Oscar Garcia-Prada which gives an overview of certain developments in the field during the decades since the book first appeared. From reviews of the 2nd Edition: "..the new edition of Professor Wells' book is timely and welcome...an excellent introduction for any mathematician who suspects that complex manifold techniques may be relevant to his work." - Nigel Hitchin, Bulletin of the London Mathematical Society "Its purpose is to present the basics of analysis and geometry on compact complex manifolds, and is already one of the standard sources for this material." - Daniel M. Burns, Jr., Mathematical Reviews