Hilbert functions of Gorenstein monomial curves
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- by Feza Arslan and Pinar Mete PDF
- Proc. Amer. Math. Soc. 135 (2007), 1993-2002 Request permission
Abstract:
It is a conjecture due to M. E. Rossi that the Hilbert function of a one-dimensional Gorenstein local ring is non-decreasing. In this article, we show that the Hilbert function is non-decreasing for local Gorenstein rings with embedding dimension four associated to monomial curves, under some arithmetic assumptions on the generators of their defining ideals in the non-complete intersection case. In order to obtain this result, we determine the generators of their tangent cones explicitly by using standard basis computations under these arithmetic assumptions and show that the tangent cones are Cohen-Macaulay. In the complete intersection case, by characterizing certain families of complete intersection numerical semigroups, we give an inductive method to obtain large families of complete intersection local rings with arbitrary embedding dimension having non-decreasing Hilbert functions.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, Middle East Technical University, Ankara, 06531 Turkey
- Address at time of publication: Department of Mathematics, Balıkesir University, Balıkesir, 10145 Turkey
- Email: pinarm@metu.edu.tr, pinarm@balikesir.edu.tr
- Received by editor(s): December 17, 2005
- Received by editor(s) in revised form: April 1, 2006
- Published electronically: March 2, 2007
- Additional Notes: The second author was supported by TÜBİTAK with grant no. TBAG-HD/108(105T543).
- Communicated by: Bernd Ulrich
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 1993-2002
- MSC (2000): Primary 13H10, 14H20; Secondary 13P10
- DOI: https://doi.org/10.1090/S0002-9939-07-08793-X
- MathSciNet review: 2299471