A natural spine for Milnor fibers of isolated plane curve singularities

Nom de l'orateur
Pablo Portilla Cuadrado
Etablissement de l'orateur
Université de Lille
Date et heure de l'exposé
Lieu de l'exposé
Salle Éole

In this talk I will explain a work in progress, joint with Baldur Sigurdsson, in which we explore an idea by A'Campo. An explicit collapsing map is constructed for each isolated hypersurface singularity using a natural connection depending on the ambient metric. The preimage of the singular point by the collapsing map yields, on each Milnor fiber, a piecewise linear spine. The combinatorics and the properties of this spine are analyzed by means of a vector field which is defined on the boundary of the real oriented blow-up of a resolution of the singularity that also resolves the polar curves. At the moment, we deal with the case of isolated plane curve singularities.