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JACOBIAN IDEALS AND THE NEWTON NON-DEGENERACY CONDITION

Published online by Cambridge University Press:  15 February 2005

Carles Bivià-Ausina
Carles Bivià-Ausina
Affiliation:
Departament de Matemàtica Aplicada, Universitat Politècnica de València, Escola Politècnica Superior d’Alcoi, Plaça Ferrándiz i Carbonell 2, 03801 Alcoi (Alacant), Spain ([email protected])
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Abstract

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In this paper we extract some conclusions about Newton non-degenerate ideals and the computation of Łojasiewicz exponents relative to this kind of ideal. This motivates us to study the Newton non-degeneracy condition on the Jacobian ideal of a given analytic function germ $f:(\mathbb{C}^n,0)\to(\mathbb{C},0)$. In particular, we establish a connection between Newton non-degenerate functions and functions whose Jacobian ideal is Newton non-degenerate.

AMS 2000 Mathematics subject classification: Primary 32S05. Secondary 57R45

Keywords

reduced ordersŁojasiewicz exponentsNewton polyhedra of ideals
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 1 , February 2005 , pp. 21 - 36
Copyright
Copyright © Edinburgh Mathematical Society 2005