Monomial curves and the Cohen-Macaulayness of their tangent cones
Author(s)
Advisor
Sertöz, SinanDate
1999Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
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.