Reduction numbers and initial ideals
Author:
Aldo Conca
Journal:
Proc. Amer. Math. Soc. 131 (2003), 10151020
MSC (2000):
Primary 13P10, 13A30; Secondary 13F20
Published electronically:
June 12, 2002
MathSciNet review:
1948090
Fulltext PDF Free Access
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Abstract: The reduction number of a standard graded algebra is the least integer such that there exists a minimal reduction of the homogeneous maximal ideal of such that . Vasconcelos conjectured that where is the initial ideal of an ideal in a polynomial ring with respect to a term order. The goal of this note is to prove the conjecture.
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Additional Information
Aldo Conca
Affiliation:
Dipartimento di Matematica, Universitá di Genova, Via Dodecaneso 35, I16146 Genova, Italia
Email:
conca@dima.unige.it
DOI:
http://dx.doi.org/10.1090/S0002993902066078
PII:
S 00029939(02)066078
Keywords:
Gr\"obner bases,
initial ideal,
reduction number,
Lexsegment ideal
Received by editor(s):
September 24, 2001
Received by editor(s) in revised form:
October 29, 2001
Published electronically:
June 12, 2002
Communicated by:
Wolmer V. Vasconcelos
Article copyright:
© Copyright 2002 American Mathematical Society
