On the cohomology of regular differential forms and dualizing sheaves
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- by Reinhold Hübl and Xiaotao Sun PDF
- Proc. Amer. Math. Soc. 126 (1998), 1931-1940 Request permission
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.References
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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
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1931-1940
- MSC (1991): Primary 13N05, 14F10
- DOI: https://doi.org/10.1090/S0002-9939-98-04499-2
- MathSciNet review: 1458879