Forme de Jordan de la Manodromie des Singularites Superisoleés de Surfaces

In this work, Artal-Bartolo calculates the Jordan form of the monodromy of surface superisolated singularities, using mixed Hodge structure. The main step in this computation is to present explicitly an embedded resolution for this family. It turns out that the topology of these singularities is sufficiently complicated to produce counterexamples to a conjecture of Yau, using the theory of projective plane curves.