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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21985

Albertini, C; Brodmann, M (2001). A bound on certain local cohomology modules and application to ample divisors. Nagoya Mathematical Journal, 163:87-106.

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## Abstract

We consider a positively graded noetherian domain for which is essentially of finite type over a perfect field of positive characteristic and we assume that the generic fibre of the natural morphism is geometrically connected, geometrically normal and of dimension . Then we give bounds on the "ranks" of the -th homogeneous part of the second local cohomology module of with respect to for . If is in addition normal, we shall see that the -modules are torsion-free for all 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.

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Kodaira vanishing theorem; graded domain English 2001 27 May 2010 16:11 27 Nov 2013 16:37 Nagoya Daigaku 0027-7630 http://www.math.nagoya-u.ac.jp/en/journal/data/2001.html#163 http://projecteuclid.org/euclid.nmj/1114631622http://www.ams.org/mathscinet-getitem?mr=1854390http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1011.13011 Web of Science®. Times Cited: 2Google Scholar™Scopus®. Citation Count: 2