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

Carles Bivià-Ausina; Santiago Encinas

doi:10.1007/s13163-012-0104-0

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arXiv · 1103.1731

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

Carles Bivià-Ausina·Santiago Encinas

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Abstract

We give an expression for the Łojasiewicz exponent of a wide class of n-tuples of ideals $(I_1,..., I_n)$ in $Ø_n$ using the information given by a fixed Newton filtration. In order to obtain this expression we consider a reformulation of Łojasiewicz 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 Łojasiewicz of its gradient map $\nabla f$ attains the maximum possible value.

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Carles Bivià-Ausina, Santiago Encinas. 2012-01-29. Lojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations. https://doi.org/10.1007/s13163-012-0104-0

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