# A polyhedral characterization of quasi-ordinary singularities

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

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.

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