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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the cohomology
of regular differential forms
and dualizing sheaves


Authors: Reinhold Hübl and Xiaotao Sun
Journal: Proc. Amer. Math. Soc. 126 (1998), 1931-1940
MSC (1991): Primary 13N05, 14F10
MathSciNet review: 1458879
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Abstract | References | Similar Articles | Additional Information

Abstract: If $Y$ is a local Dedekind scheme and $X/Y$ is a projective Cohen-Macaulay variety of relative dimension $1$, then $R^{1} f_{*} \omega ^{1}_{X/Y}$ is torsionfree if and only if $X/Y$ is arithmetically Cohen-Macaulay for a suitable embedding in $\mathbb{P}^{n}_{k}$. If $X$ is regular then $R^{1} f_{*} \omega ^{1}_{X/Y}$ is torsionfree whenever the multiplicity of the special fibre is not a multiple of the characteristic of the residue class field.


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Additional Information

Reinhold Hübl
Affiliation: Fachbereich Mathematik, Universiät Regensburg, D – 93040 Regensburg, Germany
Email: reinhold.huebl@mathematik.uni-regensburg.de

Xiaotao Sun
Affiliation: International Centre for Theoretical Physics, Mathematics Section, 34100 Trieste, Italy
Address at time of publication: Institute of Mathematics, Academia Sinica, Beijing 1000 80, People’s Republic of China
Email: xsun@ictp.trieste.it

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04499-2
PII: S 0002-9939(98)04499-2
Received by editor(s): December 18, 1996
Additional Notes: The first author was partially supported by a Heisenberg–Stipendium of the Deutsche Forschungsgemeinschaft
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1998 American Mathematical Society