Cohen-Macaulayness of tangent cones

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Arslan F.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.128, no.8, pp.2243-2251, 2000 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 128 Issue: 8
  • Publication Date: 2000
  • Doi Number: 10.1090/s0002-9939-99-05229-6
  • Journal Name: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2243-2251
  • Keywords: Cohen-Macaulay ring, monomial curve, tangent cone
  • Middle East Technical University Affiliated: No

Abstract

We give a criterion for checking the Cohen-Macaulayness of the tangent cone of a monomial curve by using the Grobner 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 greater than or equal to 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.