Institut de Mathématiques de Marseille, UMR 7373




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Polyhedral invariants for desingularization

Jeudi 10 janvier 11:00-12:00 - Bernd SCHOBER - Leibniz Universität Hannover

Polyhedral invariants for desingularization

Résumé : The goal of my talk is to present a convex geometric viewpoint on singularities and their resolution. More presciely, we discuss how the Newton polyhedron and the Hironaka polyhedron of a Weierstrass polynomial provide invariants of the singularity that reflect how ``bad" the singularities are. Here, the Hironaka polyhedron is a certain projection of the Newton polyhedron. After a brief introduction to the notions, we study the behaviour of the Hironaka polyhedron under blowing ups for curves and surfaces. Then we explain how this leads to an invariant for desingularization of surfaces in any characteristic that decreases strictly after blowing up a sufficiently nice center. We focus on the ideas and try to hide the technical details as good as possible.
This is joint work with Vincent Cossart (Versailles).

JPEG - 8.2 ko
Bernd SCHOBER

Lieu : FRUMAM - Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03

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Pour en savoir plus sur cet événement, consultez l'article Séminaire Singularités