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Lectures on vanishing theorems

Author: Hélène Esnault; Eckart Viehweg
Publisher: Basel ; Boston : Birkhäuser, 1992.
Series: DMV Seminar, Bd. 20.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book, an extended collection of lectures delivered at "Schloss Reisensburg" during the DMV-Seminar "Algebraic Geometry, 1991", aims at presenting Kodaira's vanishing theorem and several generalizations in a way which is as algebraic as possible. We develop the theory of logarithmic de Rham complexes, the use of the corresponding spectral sequence, lifting properties for manifolds and their Frobenius morphisms  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Esnault, Hélène, 1953-
Lectures on vanishing theorems.
Basel ; Boston : Birkhäuser, 1992
(DLC) 92036584
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Hélène Esnault; Eckart Viehweg
ISBN: 9783034886000 3034886004
OCLC Number: 828774988
Description: 1 online resource (164 pages) : illustrations
Contents: § 1 Kodaira's vanishing theorem, a general discussion --
§ 2 Logarithmic de Rham complexes --
§ 3 Integral parts of Q-divisors and coverings --
§ 4 Vanishing theorems, the formal set-up --
§ 5 Vanishing theorems for invertible sheaves --
§ 6 Differential forms and higher direct images --
§ 7 Some applications of vanishing theorems --
§ 8 Characteristic p methods: Lifting of schemes --
§ 9 The Frobenius and its liftings --
§ 10 The proof of Deligne and Illusie [12] --
§ 11 Vanishing theorems in characteristic p --
§ 12 Deformation theory for cohomology groups --
§ 13 Generic vanishing theorems [26], [14] --
Appendix: Hypercohomology and spectral sequences --
References.
Series Title: DMV Seminar, Bd. 20.
Responsibility: Hélène Esnault, Eckart Viehweg.

Abstract:

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  Read more...

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