Tek-terimli eğriler ve teğet konilerinin cohen-macaulay olma problemi

ABSTRACT MONOMIAL CURVES AND THE COHEN-MACAULAYNESS OF THEIR TANGENT CONES Sefa Feza Arslan Ph. D. in Mathematics Advisor: Asst. Prof. Dr. Sinan Sertöz February, 1999 In this thesis, we show that in affine /-space with / > 4, there are mono mial curves with arbitrarily large minimal number of generators of the tangent cone and still having Cohen-Macaulay tangent cone. In order to prove this result, we give complete descriptions of the defining ideals of infinitely many families of monomial curves. We determine the tangent cones of these families of curves and check the Cohen-Macaulayness of their tangent cones by using Gröbner theory. Also, we compute the Hubert functions of these families of monomial curves. Finally, we make some genus computations by using the Hubert polynomials for complete intersections in projective case and by us ing Riemann-Hurwitz formula for complete intersection curves of superelliptic type. Keywords : Monomial curves, tangent cone, Cohen-Macaulay, Gröbner basis, Hubert function, genus. IV