Frobenius amplitude and strong vanishing theorems for vector bundles
Donu Arapura
Source: Duke Math. J. Volume 121, Number 2 (2004), 231-267.
Abstract
The primary goal of this paper is to systematically exploit the method of Deligne and Illusie to obtain Kodaira-type vanishing theorems for vector bundles and, more generally, coherent sheaves on algebraic varieties. The key idea is to introduce a number that provides a cohomological measure of the positivity of a coherent sheaf called the Frobenius or F-amplitude. The F-amplitude enters into the statement of the basic vanishing theorem, and this leads to the problem of calculating, or at least estimating, this number. Most of the work in this paper is devoted to doing this in various situations.
Primary Subjects: 14F17
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1076621985
Digital Object Identifier: doi:10.1215/S0012-7094-04-12122-0
Mathematical Reviews number (MathSciNet):
MR2034642
Zentralblatt MATH identifier:
02103582
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