Gluing and Hilbert functions of monomial curves

Arslan, Feza; Mete, Pinar; Şahi̇n, Mesut

doi:10.1090/S0002-9939-08-09785-2

Gluing and Hilbert functions of monomial curves
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by Feza Arslan, Pinar Mete and Mesut Şahi̇n PDF

Proc. Amer. Math. Soc. 137 (2009), 2225-2232 Request permission

Abstract:

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.

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