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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: August 5, 1999
MathSciNet review: 1646319
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Abstract | References | Similar Articles | Additional Information

Abstract: We give an effective method to compute the regularity of a saturated ideal $I$ defining a projective curve that also determines in which step of a minimal graded free resolution of $I$ the regularity is attained.


References [Enhancements On Off] (What's this?)

  • 1. D. Bayer, The division algorithm and the Hilbert scheme, Thesis, Harvard University, Cambridge, MA, 1982.
  • 2. Dave Bayer and David Mumford, What can be computed in algebraic geometry?, Computational algebraic geometry and commutative algebra (Cortona, 1991), Sympos. Math., XXXIV, Cambridge Univ. Press, Cambridge, 1993, pp. 1–48. MR 1253986 (95d:13032)
  • 3. David Bayer and Michael Stillman, A criterion for detecting 𝑚-regularity, Invent. Math. 87 (1987), no. 1, 1–11. MR 862710 (87k:13019), http://dx.doi.org/10.1007/BF01389151
  • 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. David Eisenbud and Shiro Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), no. 1, 89–133. MR 741934 (85f:13023), http://dx.doi.org/10.1016/0021-8693(84)90092-9
  • 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.
  • 9. 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.
  • 11. Wolmer V. Vasconcelos, Computational methods in commutative algebra and algebraic geometry, Algorithms and Computation in Mathematics, vol. 2, Springer-Verlag, Berlin, 1998. With chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman. MR 1484973 (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
Published electronically: 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