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Newton filtrations, graded algebras and codimension of non-degenerate ideals

Published online by Cambridge University Press:  26 July 2002

CARLES BIVIÀ-AUSINA ,
TOSHIZUMI FUKUI  and
MARCELO JOSÉ SAIA
CARLES BIVIÀ-AUSINA
Affiliation:
Departament de Geometria i Topologia, Universitat de València, Campus de Burjassot, 46100 Burjassot (València), Spain. e-mail: bivia@uv.es
TOSHIZUMI FUKUI
Affiliation:
Department of Mathematics, Faculty of Science, Saitama University, 255 Shimo-Okubo, Urawa 338-8570, Japan. e-mail: tfukui@rimath.saitama-u.ac.jp
MARCELO JOSÉ SAIA
Affiliation:
Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo – Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil. e-mail: mjsaia@icmc.sc.usp.br
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Abstract

We investigate a generalization of the method introduced by Kouchnirenko to compute the codimension (colength) of an ideal under a certain non-degeneracy condition on a given system of generators of I. We also discuss Newton non-degenerate ideals and give characterizations using the notion of reductions and Newton polyhedra of ideals.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 133 , Issue 1 , July 2002 , pp. 55 - 75
Copyright
2002 Cambridge Philosophical Society

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