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Gluing and Hilbert functions of monomial curves

Authors: Feza Arslan, Pinar Mete and Mesut Şahi̇n
Journal: Proc. Amer. Math. Soc. 137 (2009), 2225-2232
MSC (2000): Primary 13H10, 14H20; Secondary 13P10
Published electronically: December 31, 2008
MathSciNet review: 2495255
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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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Additional Information

Feza Arslan
Affiliation: Department of Mathematics, Middle East Technical University, Ankara, 06531, Turkey

Pinar Mete
Affiliation: Department of Mathematics, Balıkesir University, Balıkesir, 10145, Turkey

Mesut Şahi̇n
Affiliation: Department of Mathematics, Atılım University, Ankara, 06836, Turkey

Keywords: Hilbert function of local ring, tangent cone, monomial curve, numerical semigroup, semigroup gluing, nice gluing, Rossi’s conjecture
Received by editor(s): July 17, 2008
Received by editor(s) in revised form: September 19, 2008
Published electronically: December 31, 2008
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.