Search

We study linear pencils of curves on normal surface singularities. Using the minimal good resolution of the pencil, we describe the topological type of generic elements of the pencil and characterize the behaviour of special elements. Furthermore, we show that the critical locus associated to the pencil is linked to the special elements. This gives a decomposition of the critical locus through the minimal good resolution and as a consequence, some information on the topological type of the critical locus.

Etant donne f un germe de fonction analytique a l'origine de C2, nous comparons la complexite topologique de la courbe discriminante de f a celle de sa courbe polaire. Let f be an analytic function germ at 0 in C2. We compare the topological complexity of the discriminant curve of f to the one of its polar curve.