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 | References | Similar Articles | Additional Information

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 ) , we give examples of a reduced hypersurface with a single isolated singularity at the origin in that require

generators for the torsion module, Torsion .

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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

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