Journal of the Mathematical Society of Japan

Łojasiewicz exponents, the integral closure of ideals and Newton polyhedra

Carles BIVlÀ-AUSINA

Full-text: Open access

Abstract

We give an upper estimate for the Łojasiewicz exponent (J,I) of an ideal JA(Kn) with respect to another ideal I in the ring A(Kn) of germs analytic functions f : (Kn,0)K, where K=C or R, using Newton polyhedrons. In particular, we give a method to estimate the Łojasiewicz exponent α0(f) of a germ fA(Kn) that can be applied when f is Newton degenerate with respect to its Newton polyhedron.

Article information

Source
J. Math. Soc. Japan, Volume 55, Number 3 (2003), 655-668.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191418995

Digital Object Identifier
doi:10.2969/jmsj/1191418995

Mathematical Reviews number (MathSciNet)
MR1978215

Zentralblatt MATH identifier
1040.32024

Subjects
Primary: 32S05: Local singularities [See also 14J17]
Secondary: 58A20: Jets

Keywords
Łojasiewicz exponents real analytic functions Newton polyhedrons

Citation

BIVlÀ-AUSINA, Carles. Łojasiewicz exponents, the integral closure of ideals and Newton polyhedra. J. Math. Soc. Japan 55 (2003), no. 3, 655--668. doi:10.2969/jmsj/1191418995. https://projecteuclid.org/euclid.jmsj/1191418995


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