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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Regularity of lex-segment ideals: Some closed formulas and applications
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by Marc Chardin and Guillermo Moreno-Socías PDF
Proc. Amer. Math. Soc. 131 (2003), 1093-1102 Request permission

Abstract:

A closed formula for computing the regularity of the lex-segment ideal in terms of the Hilbert function is given. This regularity bounds the one of any ideal with the same Hilbert function. As a consequence, we give explicit expressions to bound the regularity of a projective scheme in terms of the coefficients of the Hilbert polynomial. We also characterize, in terms of their coefficients, which polynomials are Hilbert polynomials of some projective scheme. Finally, we provide some applications to estimates for the maximal degree of generators of Gröbner bases in terms of the degrees of defining equations.
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Additional Information
  • Marc Chardin
  • Affiliation: Institut de Mathématiques, CNRS & Université Paris 6, 4, place Jussieu, F–75252 Paris cedex 05, France
  • MR Author ID: 259215
  • Email: chardin@math.jussieu.fr
  • Guillermo Moreno-Socías
  • Affiliation: LAMA, Université de Versailles & CNRS, 45, avenue des États-Unis, F–78035 Versailles cedex, France
  • Email: moreno@math.uvsq.fr
  • Received by editor(s): May 18, 2001
  • Received by editor(s) in revised form: December 4, 2001
  • Published electronically: September 5, 2002
  • Communicated by: Wolmer V. Vasconcelos
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 1093-1102
  • MSC (2000): Primary 13D02, 13D40, 13D45, 13P10
  • DOI: https://doi.org/10.1090/S0002-9939-02-06647-9
  • MathSciNet review: 1948099