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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
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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.
References:
-
- 1.
- F. Arslan, Cohen-Macaulayness of tangent cones, Proc. Amer. Math. Soc. 128 (2000) 2243-2251. MR 1653409 (2000k:13021)
- 2.
- F. Arslan, P. Mete, Hilbert functions of Gorenstein monomial curves, Proc. Amer. Math. Soc. 135 (2007) 1993-2002. MR 2299471 (2007m:13023)
- 3.
- D. Bayer, M. Stillman, Computation of Hilbert functions, Journal of Symbolic Computation 14 (1992) 31-50. MR 1177988 (94f:13018)
- 4.
- C. Delorme, Sous-monoıdes d'intersection complète de
 , Ann. Sci. École Norm. (4) 9, no. 1 (1976) 145-154. MR 0407038 (53:10821) - 5.
- D. Eisenbud, Commutative Algebra. With a View toward Algebraic Geometry, Springer-Verlag, New York, 1995. MR 1322960 (97a:13001)
- 6.
- J. Elias, The conjecture of Sally on the Hilbert function for curve singularities, Journal of Algebra 160, no. 1 (1993) 42-49. MR 1237076 (94j:13018)
- 7.
- A. Garcia, Cohen-Macaulayness of the associated graded of a semigroup ring, Comm. Algebra 10, no. 4 (1982) 393-415. MR 649344 (83k:13013)
- 8.
- G.-M. Greuel, G. Pfister, A Singular Introduction to Commutative Algebra, Springer-Verlag, Berlin, 2002. MR 1930604 (2003k:13001)
- 9.
- F. S. Macaulay, The Algebraic Theory of Modular Systems, Cambridge University Press, New York, 1916. MR 1281612 (95i:13001)
- 10.
- M. Morales, A. Thoma, Complete intersection lattice ideals, Journal of Algebra 284 (2005) 755-770. MR 2114578 (2005j:20076)
- 11.
- J.C. Rosales, On presentations of subsemigroups of
 , Semigroup Forum 55 (1997) 152-159. MR 1457760 (98h:20104) - 12.
- M. Şahin, Producing set-theoretic complete intersection monomial curves in
 , Proc. Amer. Math. Soc. 137 (2009) 1223-1233. - 13.
- A. Thoma, Construction of set-theoretic complete intersections via semigroup gluing, Contributions to Algebra and Geometry 41(1) (2000) 195-198. MR 1745589 (2001h:14059)
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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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