Polyhedral invariants for desingularization

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Date(s) - 10/01/2019
11 h 00 min - 12 h 00 min

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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).


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