Feza Arslan

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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(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)
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)
In this article we calculate the genus of a projective complete intersection of any dimension and the genus of an affine complete intersection curve of superelliptic type. The arithmetic genus of a projective complete intersection depends on the degrees of the hypersurfaces cutting it. A formula for its genus using only the degrees of these hypersurfaces is(More)
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