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Author : B. Shiffman
Publisher : Springer Science & Business Media
ISBN 13 : 1489966803
Total Pages : 183 pages
Book Rating : 4.4/5 (899 download)
Download or read book Vanishing Theorems on Complex Manifolds written by B. Shiffman and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : B. Shiffman
Publisher :
ISBN 13 : 9781489966810
Total Pages : 188 pages
Book Rating : 4.9/5 (668 download)
Download or read book Vanishing Theorems on Complex Manifolds written by B. Shiffman and published by . This book was released on 2014-09-01 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bernard Shiffman
Publisher :
ISBN 13 : 9783764332884
Total Pages : 170 pages
Book Rating : 4.3/5 (328 download)
Download or read book Vanishing Theorems on Complex Manifolds written by Bernard Shiffman and published by . This book was released on 1985-01-01 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Esnault
Publisher : Springer Science & Business Media
ISBN 13 : 9783764328221
Total Pages : 180 pages
Book Rating : 4.3/5 (282 download)
Download or read book Lectures on Vanishing Theorems written by Esnault and published by Springer Science & Business Media. This book was released on 1992-12-01 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction M. Kodaira's vanishing theorem, saying that the inverse of an ample invert ible sheaf on a projective complex manifold X has no cohomology below the dimension of X and its generalization, due to Y. Akizuki and S. Nakano, have been proven originally by methods from differential geometry ([39J and [1]). Even if, due to J.P. Serre's GAGA-theorems [56J and base change for field extensions the algebraic analogue was obtained for projective manifolds over a field k of characteristic p = 0, for a long time no algebraic proof was known and no generalization to p > 0, except for certain lower dimensional manifolds. Worse, counterexamples due to M. Raynaud [52J showed that in characteristic p > 0 some additional assumptions were needed. This was the state of the art until P. Deligne and 1. Illusie [12J proved the degeneration of the Hodge to de Rham spectral sequence for projective manifolds X defined over a field k of characteristic p > 0 and liftable to the second Witt vectors W2(k). Standard degeneration arguments allow to deduce the degeneration of the Hodge to de Rham spectral sequence in characteristic zero, as well, a re sult which again could only be obtained by analytic and differential geometric methods beforehand. As a corollary of their methods M. Raynaud (loc. cit.) gave an easy proof of Kodaira vanishing in all characteristics, provided that X lifts to W2(k).
Author :
Publisher :
ISBN 13 : 9783034886017
Total Pages : 176 pages
Book Rating : 4.8/5 (86 download)
Download or read book Lectures on Vanishing Theorems written by and published by . This book was released on 1992-12-01 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. O. Wells
Publisher : Springer Science & Business Media
ISBN 13 : 147573946X
Total Pages : 269 pages
Book Rating : 4.4/5 (757 download)
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
Author : Edoardo Vesentini
Publisher :
ISBN 13 :
Total Pages : 290 pages
Book Rating : 4.3/5 (91 download)
Download or read book Lectures on Levi Convexity of Complex Manifolds and Cohomology Vanishing Theorems written by Edoardo Vesentini and published by . This book was released on 1967 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Raymond O. Wells
Publisher : Springer Science & Business Media
ISBN 13 : 0387738916
Total Pages : 315 pages
Book Rating : 4.3/5 (877 download)
Download or read book Differential Analysis on Complex Manifolds written by Raymond O. Wells and published by Springer Science & Business Media. This book was released on 2007-10-31 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. 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. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.
Author : Edoardo Vesentini
Publisher :
ISBN 13 :
Total Pages : 262 pages
Book Rating : 4.:/5 (82 download)
Download or read book Levi Convexity of Complex Manifolds and Cohomology Vanishing Theorems written by Edoardo Vesentini and published by . This book was released on 1967 with total page 262 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 : 4.8/5 (218 download)
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 : Daniel Huybrechts
Publisher : Springer Science & Business Media
ISBN 13 : 9783540212904
Total Pages : 336 pages
Book Rating : 4.2/5 (129 download)
Download or read book Complex Geometry written by Daniel Huybrechts and published by Springer Science & Business Media. This book was released on 2005 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)
Author : Jean-Pierre Demailly
Publisher :
ISBN 13 :
Total Pages : 414 pages
Book Rating : 4.3/5 (91 download)
Download or read book School on Vanishing Theorems and Effective Results in Algebraic Geometry written by Jean-Pierre Demailly and published by . This book was released on 2001 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : 潘維凱
Publisher : Open Dissertation Press
ISBN 13 : 9781374723696
Total Pages : 102 pages
Book Rating : 4.7/5 (236 download)
Download or read book KODAIRA VANISHING THEOREM & GE written by 潘維凱 and published by Open Dissertation Press. This book was released on 2017-01-27 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "The Kodaira Vanishing Theorem and Generalizations" by 潘維凱, Wai-hoi, Bobby, Poon, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled THE KODAIRA VANISHING THEOREM AND GENERALIZATIONS submitted by Bobby Wai-hoi POON for the Degree of Master of Philosophy at the University of Hong Kong in June 2002 This thesis is a survey on the cohomology vanishing theorem by Kodaira saying thatforacompactK]ahlermanifoldM withcanonicallinebundleK andpositive holomorphiclinebundleLonM, thecohomologygroupH (M;K ŠL)=0forall q >0. Thebasicterminologyinthetheoryofcomplexmanifoldsisintroducedand the proof of the Kodaira Vanishing Theorem is followed by the use of Bochner for- mulae and identification of the cohomology group to the space of harmonic forms. Two generalizations of the Kodaira Vanishing Theorem are studied: Nadel's Van- ishing Theorem on Multiplier Ideal Sheaves and Kawamata-Viehweg's Vanishing Theorem on nef and bigQ L -estimates -divisors. By making use of H]ormander's for the @-equation, Nadel established his Vanishing Theorem. Given a complex projective manifold M and a holomorphic line bundle L equipped with a singular Hermitian metric h satisfying the positivity condition that the curvature form of L is no less than a positive multiple of the K]ahler metric on M, Nadel's Vanishing Theorem asserts that H (M;K ŠLŠI(h)) = 0 for all q > 0, where I(h) is the multiplier ideal sheaf defined by h. On the other hand, Kawamata-Viehweg's VanishingTheoremismorealgebraicinnature. Theessentialbasicnotionsinalge- braic geometry are developed for the proof of the theorem. Kawamata-Viehweg's Vanishing Theorem states that for any complex projective manifold M, L is a holomorphic line bundle which is nef and big, then H (M;K ŠL) = 0 for all Mq > 0. In this thesis the analytic and algebraic techniques for proving Kodaira's Vanishing Theorem and its generalization are studied in details and contrasted with one another. Some applications of Kodaira's Vanishing Theorem are also given. DOI: 10.5353/th_b3014773 Subjects: Complex manifolds Holomorphic functions
Author : Raymond O. Wells
Publisher : Springer
ISBN 13 : 9780387520407
Total Pages : 0 pages
Book Rating : 4.5/5 (24 download)
Download or read book Differential Analysis on Complex Manifolds written by Raymond O. Wells and published by Springer. This book was released on 2008-11-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. 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. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.
Author : Shoshichi Kobayashi
Publisher : Princeton University Press
ISBN 13 : 1400858682
Total Pages : 317 pages
Book Rating : 4.4/5 (8 download)
Download or read book Differential Geometry of Complex Vector Bundles written by Shoshichi Kobayashi and published by Princeton University Press. This book was released on 2014-07-14 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : R. Narasimhan
Publisher : Elsevier
ISBN 13 : 0080960227
Total Pages : 263 pages
Book Rating : 4.0/5 (89 download)
Download or read book Analysis on Real and Complex Manifolds written by R. Narasimhan and published by Elsevier. This book was released on 1985-12-01 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem. The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincaré and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem. Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to prove the regularity of weak solutions of elliptic equations. The chapter ends with the approximation theorem of Malgrange-Lax and its application to the proof of the Runge theorem on open Riemann surfaces due to Behnke and Stein.
Author : K. Kodaira
Publisher : Springer Science & Business Media
ISBN 13 : 1461385903
Total Pages : 476 pages
Book Rating : 4.4/5 (613 download)
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).
