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

 

Regularity of lex-segment ideals: Some closed formulas and applications


Authors: Marc Chardin and Guillermo Moreno-Socías
Journal: Proc. Amer. Math. Soc. 131 (2003), 1093-1102
MSC (2000): Primary 13D02, 13D40, 13D45, 13P10
Published electronically: September 5, 2002
MathSciNet review: 1948099
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Abstract | References | Similar Articles | Additional Information

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
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

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06647-9
PII: S 0002-9939(02)06647-9
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
Article copyright: © Copyright 2002 American Mathematical Society