Browsing by Author "Sahin, Mesut"

Now showing 1 - 3 of 3

Citation - WoS: 23
Gluing and Hilbert Functions of Monomial Curves
(Amer Mathematical Soc, 2009) Arslan, Feza; Mete, Pinar; Sahin, Mesut; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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.
Citation - WoS: 3
Citation - Scopus: 2
On Symmetric Monomial Curves in P³
(Tubitak Scientific & Technological Research Council Turkey, 2009) Sahin, Mesut; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we give an elementary proof of the fact that symmetric arithmetically Cohen-Macaulay monomial curves are set-theoretic complete intersections. The proof is constructive and provides the equations of the surfaces cutting out the monomial curve.
Citation - WoS: 7
Producing Set-Theoretic Complete Intersection Monomial Curves in Pⁿ<
(Amer Mathematical Soc, 2009) Sahin, Mesut; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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.