Cohen-macaulayness of tangent cones

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Author
Arslan F.
Date
2000Journal Title
Proceedings of the American Mathematical Society
ISSN
29939
Volume
128
Issue
8
Pages
2243 - 2251
Language
English
Type
Article
Metadata
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http://hdl.handle.net/11693/24972Abstract
We give a criterion for checking the Cohen-Macaulayness of the tangent cone of a monomial curve by using the Gröbner basis. For a family of monomial curves, we give the full description of the defining ideal of the curve and its tangent cone at the origin. By using this family of curves and their extended versions to higher dimensions, we prove that the minimal number of generators of a Cohen-Macaulay tangent cone of a monomial curve in an affine l-space can be arbitrarily large for l ≥ 4 contrary to the l = 3 case shown by Robbiano and Valla. We also determine the Hubert series of the associated graded ring of this family of curves and their extended versions. © 2000 American Mathematical Society.