Cohen-Macaulayness of tangent cones

Author:
Feza Arslan

Journal:
Proc. Amer. Math. Soc. **128** (2000), 2243-2251

MSC (1991):
Primary 14H20; Secondary 13H10, 13P10

DOI:
https://doi.org/10.1090/S0002-9939-99-05229-6

Published electronically:
November 29, 1999

MathSciNet review:
1653409

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Abstract | References | Similar Articles | Additional Information

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 -space can be arbitrarily large for contrary to the 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:
https://doi.org/10.1090/S0002-9939-99-05229-6

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