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.References
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Additional Information
- Feza Arslan
- Affiliation: Department of Mathematics, Middle East Technical University, Ankara, 06531, Turkey
- Email: sarslan@metu.edu.tr
- Pinar Mete
- Affiliation: Department of Mathematics, Balıkesir University, Balıkesir, 10145, Turkey
- Email: pinarm@balikesir.edu.tr
- Mesut Şahi̇n
- Affiliation: Department of Mathematics, Atılım University, Ankara, 06836, Turkey
- Email: mesutsahin@gmail.com
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2225-2232
- MSC (2000): Primary 13H10, 14H20; Secondary 13P10
- DOI: https://doi.org/10.1090/S0002-9939-08-09785-2
- MathSciNet review: 2495255