TORSION OF DIFFERENTIALS OF AFFINE QUASI-HOMOGENEOUS HYPERSURFACES

In this paper we prove that the torsion modules of the module of Kaehler differentials of affine hypersurfaces defined by a reduced quasi-homogeneous polynomial with an isolated singularity at the origin are cyclic. We give explicit expressions for generators. Moreover, we exhibit an isomorphism bet...

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Bibliographic Details
Published in:	The Rocky Mountain journal of mathematics Vol. 26; no. 1; pp. 229 - 236
Main Author:	MICHLER, RUTH I.
Format:	Journal Article
Language:	English
Published:	The Rocky Mountain Mathematics Consortium 1996 Rocky Mountain Mathematics Consortium
Subjects:	Algebra Differentials Hypersurfaces Isolated singularities Mathematical theorems Polynomials
Online Access:	Get full text
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Summary:	In this paper we prove that the torsion modules of the module of Kaehler differentials of affine hypersurfaces defined by a reduced quasi-homogeneous polynomial with an isolated singularity at the origin are cyclic. We give explicit expressions for generators. Moreover, we exhibit an isomorphism between the torsion submodule of $\Omega _{A/K}^N$ and $\Omega _{A/K}^{N - 1}$ for such hypersurfaces. A — D — E singularities provide examples of such hypersurfaces.
ISSN:	0035-7596 1945-3795
DOI:	10.1216/rmjm/1181072113