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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 number of generators of the torsion module of differentials


Author: Ruth I. Michler
Journal: Proc. Amer. Math. Soc. 129 (2001), 639-646
MSC (2000): Primary 13N05, 14F10
Published electronically: August 29, 2000
MathSciNet review: 1707527
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Abstract:

In this paper we study the (minimum) global number of generators of the torsion module of differentials of affine hypersurfaces with only isolated singularities. We show that for reduced plane curves the torsion module of differentials can be generated by at most two elements, whereas for higher codimensions there is no universal upper bound. We then proceed to give explicit examples. In particular (when $N \geq 5$) , we give examples of a reduced hypersurface with a single isolated singularity at the origin in $\mathbf{A}^{N}_{K}$ that require

\begin{displaymath}\frac{N!}{2} + N(N-1)/2\end{displaymath}

generators for the torsion module, Torsion $(\Omega_{A/K}^{N-1})$.


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Additional Information

Ruth I. Michler
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203-5116
Email: michler@unt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05572-6
PII: S 0002-9939(00)05572-6
Received by editor(s): December 11, 1998
Received by editor(s) in revised form: May 10, 1999
Published electronically: August 29, 2000
Additional Notes: The author was partially supported by NSF-DMS 9510654 and a Texas Advanced Research Project Grant from the state of Texas. The author thanks Prof. A. Iarrobino for helpful discussions
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society