We give a criterion for checking the Cohen-Macaulayness of the tangent cone of a monomial curve by using Grr obner basis. For a family of monomial curves, we give the full description of the deening 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 minimal… (More)
For the projective case we exhibit a practical method for calculating the Hilbert function of a complete intersection of any dimension. In the aane case we deal with complete intersection curves of superel-liptic type. With the help of Grobner techniques we give an explicit formula for the geometric genus.