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Article Citation - WoS: 24Gluing and Hilbert Functions of Monomial Curves(Amer Mathematical Soc, 2009) Arslan, Feza; Mete, Pinar; Sahin, MesutIn this article, by using the technique of gluing semigroups, we give infinitely many families of 1-dimensional local rings with non-decreasing Hilbert functions. More significantly, these are local rings whose associated graded rings are not necessarily Cohen-Macaulay. In this sense, we give an effective technique for constructing large families of 1-dimensional Gorenstein local rings associated to monomial curves, which support Rossi's conjecture saying that every Gorenstein local ring has a non-decreasing Hilbert function.Article Citation - WoS: 7Producing Set-Theoretic Complete Intersection Monomial Curves in Pn<(Amer Mathematical Soc, 2009) Sahin, MesutIn this paper we describe an algorithm for producing infinitely many examples of set-theoretic complete intersection monomial curves in Pn+1, starting with a single set-theoretic complete intersection monomial curve in P-n. Moreover we investigate the numerical criteria to decide when these monomial curves can or cannot be obtained via semigroup gluing.
