Seminar of Algebra

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$\mu$-constant families of isolated hypersurface singularities and simultaneous embedded desingularization

Mark Spivakovsky (CNRS, Institut de Mathématiques de Toulouse and LaSol, Cuernavaca)
Departamento de Álgebra
Fri, 7 jun 2019 11:30
Mark Spivakovsky es Directeur de Recherche del CNRS. Sus áreas de interés son Geometría algebraica, álgebra conmutativa, especialmente la resolución de singularidades, teoría de valoraciones y uniformización local

We will begin this talk with a brief summary of different notions of equisingularity in families of isolated hypersurface singlarities, concentrating on various notions of simultaneous deisngularization.

We will then report on joint work in progress with Max Leyton and Hussein Mourtada. The starting point of this work is a 1980 paper by Yujiro Kawamata in which the author claims to relate the existence of simultaneous embedded resolution in a family to the property of it being $\mu^{ * }$-constant. Inspired by this paper, we formulated two conjectures relating the notions of $\mu$-constant, $\mu^{ * }$-constant and simultaneous embedded resolution. We will illustrate the first conjecture with the example of Birançon -- Speder.