Permanent URL to this publication: http://dx.doi.org/10.5167/uzh21985
Albertini, C; Brodmann, M (2001). A bound on certain local cohomology modules and application to ample divisors. Nagoya Mathematical Journal, 163:87106.

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Abstract
We consider a positively graded noetherian domain $R = \bigoplus_{n \in \BN_{0}} R_{n}$ for which $R_{0}$ is essentially of finite type over a perfect field $K$ of positive characteristic and we assume that the generic fibre of the natural morphism $\pi : Y = \Proj(R) \to Y_{0} = \Spec(R_{0})$ is geometrically connected, geometrically normal and of dimension $> 1$. Then we give bounds on the "ranks" of the $n$th homogeneous part $H^{2}_{R_{+}} (R)_{n}$ of the second local cohomology module of $R$ with respect to $R_{+} := \bigoplus_{m > 0} R_{m}$ for $n < 0$. If $Y$ is in addition normal, we shall see that the $R_{0}$modules $H^{2}_{R_{+}} (R)_{n}$ are torsionfree for all $n < 0$ and in this case our bounds on the ranks furnish a vanishing result. From these results we get bounds on the first cohomology of ample invertible sheaves in positive characteristic.
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Additional indexing
Item Type:  Journal Article, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
Dewey Decimal Classification:  510 Mathematics 
Uncontrolled Keywords:  Kodaira vanishing theorem; graded domain 
Language:  English 
Date:  2001 
Deposited On:  27 May 2010 16:11 
Last Modified:  05 Apr 2016 13:25 
Publisher:  Nagoya Daigaku 
ISSN:  00277630 
Official URL:  http://www.math.nagoyau.ac.jp/en/journal/data/2001.html#163 
Related URLs:  http://projecteuclid.org/euclid.nmj/1114631622 http://www.ams.org/mathscinetgetitem?mr=1854390 http://www.zentralblattmath.org/zbmath/search/?q=an%3A1011.13011 
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