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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:   Print book : English
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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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Hélène Esnault; Eckart Viehweg
ISBN: 3764328223 9783764328221 0817628223 9780817628222
OCLC Number: 26719227
Description: 164 pages : illustrations ; 24 cm.
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.
Series Title: DMV Seminar, Bd. 20.
Responsibility: Hélène Esnault, Eckart Viehweg.
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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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