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Seminario de Algebra y Combinatoria

Seminario de Algebra y Combinatoria

Viernes 18 de marzo de 2016

Módulo 17, aula 420, 11:30 hr.

Bernd Schober

(Leibniz Universität Hannover)

A polyhedral characterization of quasi-ordinary singularities

Resumen:  Let $X$ be an irreducible hypersurface given by a polynomial $f in K{x_1, ldots, x_d}[z]$, where $K$ denotes an algebraically closed field of characteristic zero. The variety $X$ is called quasi-ordinary with respect to the projection to the affine space defined by $K{x_1, ldots, x_d}$ if the discriminant of $f$ is a monomial times a unit. In my talk I am going to present the construction of an invariant that allows to detect whether a given polynomial $f$ (with fixed projection) defines a quasi-ordinary singularity. This involves a weighted version of Hironaka's characteristic polyhedron and successive embeddings of the singularity in affine spaces of higher dimensions. Further, I will explain how the construction permits to view $X$ as an "overweight deformation" of a toric variety which leads then to the proof of our characterization.

Localización Viernes 18 de marzo de 2016 Módulo 17, aula 420, 11:30 hr.