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)
It is a conjecture due to M. E. Rossi that the Hilbert function of a one-dimensional Gorenstein local ring is non-decreasing. In this article, we show that the Hilbert function is non-decreasing for local Gorenstein rings with embedding dimension four associated to monomial curves, under some arithmetic assumptions on the generators of their defining ideals… (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.
Zikê zaroka tijeye lê zimanê wan nagere... iii ACKNOWLEDGEMENTS First and foremost, I would like to express my deep gratitude to my advisor John Etnyre. His constant support, guidance and availability throughout the three years of graduate school made this work possible. There is no question that I will always feel very lucky, like all others, for being his… (More)