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

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.

arXiv comment25 pages. Updated with minor changes

References in corpus (2)

• The Łojasiewicz exponent of a set of weighted homogeneous ideals
• Lojasiewicz exponents and resolution of singularities

Cited by in corpus (1)

• Resolution of singularities and geometric proofs of the Lojasiewicz inequalities