Algebra-Algebraic and Aritmetic Geometry Seminar
The medial axis of the Milnor fiber
Speaker: Pablo Portilla (UPM)Date: Monday, 09 March 2026 - 11:00Place: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Online: Teams (contactar con ana.bravo@uam.es)
Abstract:
Let f(x,y) define an isolated plane singularity at the origin.
In this talk we explore some consequences of the existence of a flat metric induced on the Milnor fiber of f by the associated complex Hamiltonian vector field. With the help of this metric we can uniformly close each Milnor fiber using conical ends and define a spine on it via the classical method of the medial axis. This method depends only on the metric. The spine is subanalytic and comes equipped with a retraction from the boundary onto it. In an ongoing joint work with Norbert A'Campo we explore the geometry of the versal unfolding via these spines.
