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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cohen-Macaulayness of tangent cones


Author: Feza Arslan
Journal: Proc. Amer. Math. Soc. 128 (2000), 2243-2251
MSC (1991): Primary 14H20; Secondary 13H10, 13P10
Published electronically: November 29, 1999
MathSciNet review: 1653409
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Abstract: 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 $l \geq 4$ contrary to the $l=3$ case shown by Robbiano and Valla. We also determine the Hilbert series of the associated graded ring of this family of curves and their extended versions.


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Additional Information

Feza Arslan
Affiliation: Department of Mathematics, Bilkent University, Ankara, Turkey 06533
Address at time of publication: Department of Mathematics, METU, Ankara, Turkey 06531
Email: sarslan@fen.bilkent.edu.tr, feza@arf.math.metu.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05229-6
PII: S 0002-9939(99)05229-6
Keywords: Cohen-Macaulay ring, monomial curve, tangent cone
Received by editor(s): May 1, 1998
Received by editor(s) in revised form: September 18, 1998
Published electronically: November 29, 1999
Additional Notes: The author was supported by TÜBİTAK BDP Grant.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society