Bernd Schober – A polyhedral characterization of quasi-ordinary singularities

Carte non disponible

Date/heure
Date(s) - 03/03/2016
14 h 00 min - 15 h 00 min

Catégories Pas de Catégories


Let X be an irreducible hypersurface given by a polynomial f in K[ [ x1,…, xd ] ][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[ [ x1,…, xd ] ] 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.[

Bernd SCHOBER – A polyhedral characterization of quasi-ordinary singularities

Carte non disponible

Date/heure
Date(s) - 03/03/2016
14 h 00 min - 15 h 00 min

Catégories Pas de Catégories


Let X be an irreducible hypersurface given by a polynomial f in K[ [ x1,…, xd ] ][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[ [ x1,…, xd ] ] 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. https://sites.google.com/site/scb16105/ Bernd SCHOBER [