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

Autores UPV
Revista Revista Matemática Complutense


We give an expression for the Lojasiewicz exponent of a wide class of n-tuples of ideals (I1, . . . , In) in O_n using the information given by a fixed Newton filtration. In order to obtain this expression we consider a reformulation of Lojasiewicz exponents in terms of Rees mixed multiplicities. As a consequence, we obtain a wide class of semi-weighted homogeneous functions f : (Cn, 0-->(C, 0) for which the Lojasiewicz of its gradient map attains the maximum possible value.