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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.

## Citations

2 citations in Web of Science®
2 citations in Scopus®