Author: B. ShiffmanPublisher: Springer Science & Business Media
ISBN: 1489966803
Category : Science
Languages : en
Pages : 183
Book Description
Vanishing Theorems on Complex Manifolds
Author: B. ShiffmanPublisher: Springer Science & Business Media
ISBN: 1489966803
Category : Science
Languages : en
Pages : 183
Book Description
Vanishing Theorems on Complex Manifolds
Author: B. ShiffmanPublisher:
ISBN: 9781489966810
Category :
Languages : en
Pages : 188
Book Description
Vanishing Theorems on Complex Manifolds
Author: Bernard ShiffmanPublisher:
ISBN: 9783764332884
Category : Complex manifolds
Languages : en
Pages : 170
Book Description
Lectures on Vanishing Theorems
Author: EsnaultPublisher: Springer Science & Business Media
ISBN: 9783764328221
Category : Science
Languages : en
Pages : 180
Book Description
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).
Lectures on Vanishing Theorems
Author: Differential Analysis on Complex Manifolds
Author: R. O. WellsPublisher: Springer Science & Business Media
ISBN: 147573946X
Category : Mathematics
Languages : en
Pages : 269
Book Description
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
Differential Analysis on Complex Manifolds
Author: Raymond O. WellsPublisher: Springer Science & Business Media
ISBN: 0387738916
Category : Mathematics
Languages : en
Pages : 315
Book Description
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.
Lectures on Levi Convexity of Complex Manifolds and Cohomology Vanishing Theorems
Author: Edoardo VesentiniPublisher:
ISBN:
Category : Complex manifolds
Languages : en
Pages : 290
Book Description
Complex Manifolds
Author: James A. MorrowPublisher: American Mathematical Soc.
ISBN: 082184055X
Category : Mathematics
Languages : en
Pages : 210
Book Description
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: Edoardo Vesentini