THE THIRTEENTH COLLOQUIUMFEST

Speaker:
Santiago Encinas (Universidad de Valladolid, Spain)

Title:
Lojasiewicz exponent using Newton filtrations

Abstract:
The Lojasiewicz exponent of an ideal I with respect to another ideal J,
denoted by L_J(I), is a real number and it is originally defined in
analytical terms, where I and J are ideals of complex analytic function
germs for C^n to C. It is known that L_J(I) may be expressed in terms of
the integral closure of the ideals I and J. The definition of the
Lojasiewicz exponent may be extended to n-uples of ideals I_1,...,I_n,
say L_J(I_1,...,I_n) in terms of Rees mixed multiplicities.

We will give an expression for the Lojasiewicz exponent of a wide class
of n-uples of ideals (I_1,\dots, I_n) using the information given by a
fixed Newton filtration.

The above result provides a wide class of semi-weighted homogeneous
functions for which the Lojasiewicz exponent of its gradient map attains
the maximum possible value.

This is a joint work with Carles Bivia-Ausina