On the number of generators of the torsion module of differentials
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- by Ruth I. Michler PDF
- Proc. Amer. Math. Soc. 129 (2001), 639-646 Request permission
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 \[ \frac {N!}{2} + N(N-1)/2\] generators for the torsion module, $\operatorname {Torsion}(\Omega _{A/K}^{N-1})$.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 639-646
- MSC (2000): Primary 13N05, 14F10
- DOI: https://doi.org/10.1090/S0002-9939-00-05572-6
- MathSciNet review: 1707527