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      Cohen-macaulayness of tangent cones

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      Author
      Arslan F.
      Date
      2000
      Journal Title
      Proceedings of the American Mathematical Society
      ISSN
      29939
      Volume
      128
      Issue
      8
      Pages
      2243 - 2251
      Language
      English
      Type
      Article
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      Please cite this item using this persistent URL
      http://hdl.handle.net/11693/24972
      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 ≥ 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.
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