Lectures on Vanishing Theorems - Oberwolfach Seminars 20 (Paperback)
  • Lectures on Vanishing Theorems - Oberwolfach Seminars 20 (Paperback)
zoom

Lectures on Vanishing Theorems - Oberwolfach Seminars 20 (Paperback)

(author), (author)
£69.99
Paperback 166 Pages / Published: 01/12/1992
  • We can order this from the publisher

UK delivery within 3-4 weeks

  • This item has been added to your basket
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).

Publisher: Birkhauser Verlag AG
ISBN: 9783764328221
Number of pages: 166
Weight: 350 g
Dimensions: 244 x 170 x 9 mm
Edition: 1992 ed.

You may also be interested in...

Fractals: A Very Short Introduction
Added to basket
Elliptic Tales
Added to basket
£12.99
Paperback
Visual Complex Analysis
Added to basket
Trigonometry Workbook For Dummies
Added to basket
Drawing Geometry
Added to basket
£12.99
Paperback
Platonic and Archimedean Solids
Added to basket
Ruler and Compass
Added to basket
£5.99
Paperback
Symmetry: A Very Short Introduction
Added to basket
Algebraic Geometry
Added to basket
Trigonometry For Dummies, 2nd Edition
Added to basket
Introduction to Topology
Added to basket
Challenging Problems in Geometry
Added to basket
Advanced Euclidean Geometry
Added to basket
Elementary Geometry
Added to basket
£59.00
Paperback
Euclid's Elements
Added to basket
£21.99
Paperback

Please sign in to write a review

Your review has been submitted successfully.