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Gluing and Hilbert functions of monomial curves
Author(s):
Feza
Arslan;
Pinar
Mete;
Mesut
Sahin
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2225-2232.
MSC (2000):
Primary 13H10, 14H20;
Secondary 13P10
Posted:
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
Email:
sarslan@metu.edu.tr
Pinar
Mete
Affiliation:
Department of Mathematics, Balikesir University, Balikesir, 10145, Turkey
Email:
pinarm@balikesir.edu.tr
Mesut
Sahin
Affiliation:
Department of Mathematics, Atilim University, Ankara, 06836, Turkey
Email:
mesutsahin@gmail.com
DOI:
10.1090/S0002-9939-08-09785-2
PII:
S 0002-9939(08)09785-2
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
Posted:
December 31, 2008
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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