DEFORMATIONS WITH CONSTANT MILNOR NUMBER AND MULTIPLICITY OF COMPLEX HYPERSURFACES The first named author is partially supported by CNPq-Grant 30055692-6.

Abstract

Abstract.We investigate the constancy of the Milnor number of one parameter deformations of holomorphic germs of functions f : ‫ރ(‬ n , 0) → ‫,ރ(‬ 0) with isolated singularity, in terms of some Newton polyhedra associated to such germs.When the Jacobian ideals J(are non-degenerate on some fixed Newton polyhedron + , we show that this family has constant Milnor number for small values of t, if and only if all germs g s have non-decreasing -order with respect to f . As a consequence of these results we give a positive answer to Zariski's question for Milnor constant families satisfying a non-degeneracy condition on the Jacobian ideals.

Deformations with constant Lê numbers and multiplicity of nonisolated hypersurface singularities

“…. But in each case, (C1)-(C4), the Zariski multiplicity conjecture is true if we deal with families of isolated singularities (the references for that are [1], [6], [15], [17], [19], [21]). In other words, the family {h t + z N 1 1…”