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Castelnuovo-Mumford regularity and the reduction number of some monomial curves
Author(s):
Michael
Hellus;
Lê
Tuân
Hoa;
Jürgen
Stückrad
Journal:
Proc. Amer. Math. Soc.
138
(2010),
27-35.
MSC (2000):
Primary 13A30, 13D45
Posted:
August 13, 2009
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Abstract:
We compare the Castelnuovo-Mumford regularity and the reduction number of some classes of monomial projective curves with at most one singular point. Furthermore, for smooth monomial curves we prove an upper bound on the regularity which is stronger than the one given by L'vovsky.
References:
-
- 1.
- J. L. Ramírez Alfonsín, The Diophantine Frobenius problem, Oxford Univ. Press, Oxford, 2005. MR 2260521 (2007i:11052)
- 2.
- I. Bermejo, P. Gimenez and M. Morales, Castelnuovo-Mumford regularity of projective monomial varieties of codimension two, J. Symbolic Comput. 41 (2006), no. 10, 1105-1124. MR 2262086 (2007i:14046)
- 3.
- H. Bresinsky, Monomial Buchsbaum ideals in
 , Manuscripta Math. 47 (1984), no. 1-3, 105-132. MR 744315 (85j:14090) - 4.
- D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), no. 1, 89-133. MR 741934 (85f:13023)
- 5.
- S. Goto, N. Suzuki and K. Watanabe, On affine semigroup rings, Japan. J. Math. (N.S.) 2 (1976), no. 1, 1-12. MR 0450257 (56:8553)
- 6.
- L. Gruson, R. Lazarsfeld and C. Peskine, On a theorem of Castelnuovo, and the equations defining space curves, Invent. Math. 72 (1983), no. 3, 491-506. MR 704401 (85g:14033)
- 7.
- J. Herzog and T. Hibi, Castelnuovo-Mumford regularity of simplicial semigroup rings with isolated singularity, Proc. Amer. Math. Soc. 131 (2003), no. 9, 2641-2647 (electronic). MR 1974318 (2004j:13025)
- 8.
- L. T. Hoa and J. Stückrad, Castelnuovo-Mumford regularity of simplicial toric rings, J. Algebra 259 (2003), no. 1, 127-146. MR 1953712 (2003j:13024)
- 9.
- S. L
 vovsky, On inflection points, monomial curves, and hypersurfaces containing projective curves, Math. Ann. 306 (1996), no. 4, 719-735. MR 1418349 (99e:14033) - 10.
- Macaulay 2 (a computer algebra system). Available from http://www.math.uiuc.edu/ Macaulay2/.
- 11.
- Ngô Viêt Trung and Lê Tuân Hoa, Affine semigroups and Cohen-Macaulay rings generated by monomials, Trans. Amer. Math. Soc. 298 (1986), no. 1, 145-167. MR 857437 (87j:13032)
- 12.
- Ngô Viêt Trung, Reduction exponent and degree bound for the defining equations of graded rings, Proc. Amer. Math. Soc. 101 (1987), no. 2, 229-236. MR 902533 (89i:13031)
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Additional Information:
Michael
Hellus
Affiliation:
Fakultät für Mathematik und Informatik, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany
Email:
Michael.Hellus@math.uni-leipzig.de
Lê
Tuân
Hoa
Affiliation:
Institute of Mathematics Hanoi, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam
Email:
lthoa@math.ac.vn
Jürgen
Stückrad
Affiliation:
Fakultät für Mathematik und Informatik, Universität Leipzig, Augustusplatz 10/11, D-04109 Leipzig, Germany
Email:
stueckrad@math.uni-leipzig.de
DOI:
10.1090/S0002-9939-09-10055-2
PII:
S 0002-9939(09)10055-2
Keywords:
Castelnuovo-Mumford regularity,
reduction number,
Eisenbud-Goto conjecture
Received by editor(s):
October 5, 2007,
Received by editor(s) in revised form:
September 4, 2008, and April 2, 2009
Posted:
August 13, 2009
Additional Notes:
The second author was supported by the NAFOSTED (Vietnam) and Max-Planck Institute for Mathematics in the Sciences (Germany). He would like to thank the MIS for their financial support and hospitality.
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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