Browsing by Subject "Monomial curves"
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Item Open Access Betti numbers for certain Cohen–Macaulay tangent cones(Cambridge University Press, 2019) Şahin, M.; Şahin, NilWe compute Betti numbers for a Cohen–Macaulay tangent cone of a monomial curve in the affine 4-space corresponding to a pseudo-symmetric numerical semigroup. As a byproduct, we also show that for these semigroups, being of homogeneous type and homogeneous are equivalent properties.Item Open Access Monomial curves and the Cohen-Macaulayness of their tangent cones(Bilkent University, 1999) Arslan, Sefa FezaIn this thesis, we show that in affine /-space with / > 4, there are monomial 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 Grobner theory. Also, we compute the Hilbert functions of these families of monomial curves. Finally, we make some genus computations by using the Hilbert polynomials for complete intersections in projective case and by using Riemann-Hurwitz formula for complete intersection curves of superelliptic type.Item Open Access On the minimal number of elements generating an algebraic set(Bilkent University, 2002) Şahin, MesutIn this thesis we present studies on the general problem of finding the minimal number of elements generating an algebraic set in n-space both set and ideal theoretically.