Lectures on Vanishing Theorems

Name: Lectures on Vanishing Theorems
Brand: Birkhauser Verlag AG
SKU: 9783764328221
Price: 363.3 PLN
Availability: InStock

Papers of a DMV-seminar on algebraic geometry, Schloß Reisensburg, October 13-19, 1991

Autor: Helene Esnault, Eckart Viehweg

Język:

Oprawa: Miękka

Wydawca: Birkhauser Verlag AG

Dostępność: Dostępna u dostawcy

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Introduction M. Kodaira's vanishing theorem, saying that the inverse of an ample invert ible sheaf o...

Informacje o książce

Autor

Helene Esnault, Eckart Viehweg

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

1992

strony

166

EAN

9783764328221

ISBN

3764328223

Enbook ID

06930121

Wydawca

Birkhauser Verlag AG

Waga

350

Wymiary

170 x 244 x 10

Pełny opis

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).

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Lectures on Vanishing Theorems

Papers of a DMV-seminar on algebraic geometry, Schloß Reisensburg, October 13-19, 1991

Informacje o książce

Pełny opis

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