Lojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations

Details Lojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations Lojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations

2011-03-09

arxiv.org/abs/1103.1731v2

Mathematics

Algebraic Geometry

25 pages. Updated with minor changes

Scientific paper

We give an expression for the {\L}ojasiewicz exponent of a wide class of n-tuples of ideals $(I_1,..., I_n)$ in $\O_n$ using the information given by a fixed Newton filtration. In order to obtain this expression we consider a reformulation of {\L}ojasiewicz exponents in terms of Rees mixed multiplicities. As a consequence, we obtain a wide class of semi-weighted homogeneous functions $(\mathbb{C}^n,0)\to (\mathbb{C},0)$ for which the {\L}ojasiewicz of its gradient map $\nabla f$ attains the maximum possible value.

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