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On Castelnuovo-Mumford regularity
of projective curves
Authors:
Isabel Bermejo and Philippe Gimenez
Journal:
Proc. Amer. Math. Soc. 128 (2000), 1293-1299
MSC (1991):
Primary 13D45; Secondary 14Q05, 13D40
Posted:
August 5, 1999
MathSciNet review:
1646319
Full-text PDF Free Access
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Additional Information
Abstract: We give an effective method to compute the regularity of a saturated ideal  defining a projective curve that also determines in which step of a minimal graded free resolution of  the regularity is attained.
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(95d:13032)
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Bayer and Michael
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Eisenbud and Shiro
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Algebra 88 (1984), no. 1, 89–133. MR 741934
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- 1.
- D. Bayer, The division algorithm and the Hilbert scheme, Thesis, Harvard University, Cambridge, MA, 1982.
- 2.
- D. Bayer and D. Mumford, What can be computed in Algebraic Geometry? In: Computational Algebraic Geometry and Commutative Algebra, Proceedings Cortona 1991 (D. Eisenbud and L. Robbiano, Eds.), Cambridge University Press, 1993, 1-48. MR 95d:13032
- 3.
- D. Bayer and M. Stillman, A criterion for detecting
 -regularity, Invent. Math. 87 (1987) 1-11. MR 87k:13019
- 4.
- D. Bayer and M. Stillman, Macaulay, a system for computation in Algebraic Geometry and Commutative Algebra, 1992, available via anonymous ftp from math.harvard.edu.
- 5.
- I. Bermejo and M. Lejeune-Jalabert, Sur la compléxité du calcul des projections d'une courbe projective, to appear in Comm. in Algebra.
- 6.
- D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, Graduate Texts in Mathematics 150, Springer, Berlin, Heidelberg, New York, 1995.
- 7.
- D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicities, J. Algebra 88 (1984) 89-133. MR 85f:13023
- 8.
- G.M. Greuel, G. Pfister and H. Schoenemann, Singular, a system for computation in Algebraic Geometry and Singularity Theory, 1995, available via anonymous ftp from helios.mathematik.uni-kl.de.
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- M. Lejeune-Jalabert, Effectivité de calculs polynomiaux, Cours de D.E.A., Institut Fourier, Grenoble, 1984-85.
- 10.
- P. Schenzel, On the use of Local Cohomology in Algebra and Geometry, In: Six Lectures on Commutative Algebra (J. Elias, J.M. Giral, R.M. Miró-Roig and S. Zarzuela, Eds.), Progress in Mathematics 166, Birkhauser, Boston, 1998.
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- W.V. Vasconcelos, Computational Methods in Commutative Algebra and Algebraic Geometry, Algorithms and Computation in Mathematics 2, Springer, Berlin, Heidelberg, New York, 1998. MR 99c:13048
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Additional Information
Isabel Bermejo
Affiliation:
Departamento de Matematica Fundamental, Facultad de Matematicas, Universidad de La Laguna, 38271-La Laguna, Tenerife, Spain
Email:
ibermejo@ull.es
Philippe Gimenez
Affiliation:
Departamento de Algebra, Geometria y Topologia, Facultad de Ciencias, Universidad de Valladolid, 47005-Valladolid, Spain
Email:
pgimenez@wamba.cpd.uva.es
DOI:
http://dx.doi.org/10.1090/S0002-9939-99-05184-9
PII:
S 0002-9939(99)05184-9
Keywords:
Regularity,
projective curves,
Hilbert functions
Received by editor(s):
June 23, 1998
Posted:
August 5, 1999
Additional Notes:
The first author was supported in part by D.G.U.I., Gobierno de Canarias.
The second author was supported in part by D.G.I.C.Y.T., PB94-1111-C02-01.
Communicated by:
Wolmer V. Vasconcelos
Article copyright:
© Copyright 2000 American Mathematical Society
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