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Regularity of lex-segment ideals: Some closed formulas and applications
Author(s):
Marc
Chardin;
Guillermo
Moreno-Socías
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1093-1102.
MSC (2000):
Primary 13D02, 13D40, 13D45, 13P10
Posted:
September 5, 2002
MathSciNet review:
1948099
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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:
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
Posted:
September 5, 2002
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
2002,
American Mathematical Society
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