Felix Delgado

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. Then 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,
information on the topological type of the critical locus.