Sur le lieu polaire de morphismes analytiques complexes

Abstract

Let (S, 0) be a normal two-dimensional analytic germ and ϕ = (f, g) : (S, 0)→( C 2, 0) be a germ of a finite analytic morphism. We prove that, in a good resolution of (S, 0) in which the total transform of (fg) −1 ( 0) has only normal crossings, the strict transform of the polar locus of ϕ intersects the exceptional curve in some well-defined regions, of which we give a numerical characterization. These results generalize those of [7].