Browsing by Subject "Cohen-Macaulay rings."

Now showing 1 - 2 of 2

Open Access
Monomial curves and the Cohen-Macaulayness of their tangent cones
(1999) Arslan, Sefa Feza
In 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.
Open Access
On complete intersections and connectedness
(2002) Önal, Meltem
In this thesis, we study the relation between connectedness and complete intersections. We describe the concept of connectedness in codimension k. We also study the basic facts about Cohen-Macaulay rings, and give some applications about these rings and complete intersections. Finally, we show that certain rational curves of degree ≥ 4 in the projective 3-space are settheoretical complete intersections in all prime characteristics p > 0.