Lectures on Vanishing Theorems

Lectures on Vanishing Theorems
Author :
Publisher : Birkhäuser
Total Pages : 173
Release :
ISBN-10 : 9783034886000
ISBN-13 : 3034886004
Rating : 4/5 (004 Downloads)

Book Synopsis Lectures on Vanishing Theorems by : Esnault

Download or read book Lectures on Vanishing Theorems written by Esnault and published by Birkhäuser. This book was released on 2012-12-06 with total page 173 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).

Lectures on Vanishing Theorems Related Books

Lectures on Vanishing Theorems
Language: en
Pages: 173
Authors: Esnault
Categories: Science
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

GET EBOOK

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 th
Lectures on Vanishing Theorems
Language: en
Pages: 164
Authors: Hélène Esnault
Categories: Mathematics
Type: BOOK - Published: 1992 - Publisher: Birkhauser

GET EBOOK

Snowbird Lectures in Algebraic Geometry
Language: en
Pages: 202
Authors: Ravi Vakil
Categories: Mathematics
Type: BOOK - Published: 2005 - Publisher: American Mathematical Soc.

GET EBOOK

A significant part of the 2004 Summer Research Conference on Algebraic Geometry (Snowbird, UT) was devoted to lectures introducing the participants, in particul
Higher Dimensional Complex Varieties
Language: en
Pages: 400
Authors: Marco Andreatta
Categories: Mathematics
Type: BOOK - Published: 1996 - Publisher: Walter de Gruyter

GET EBOOK

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a
Sheaves in Topology
Language: en
Pages: 253
Authors: Alexandru Dimca
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

GET EBOOK

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds. This introduction to the subjec