A polyhedral characterization of quasi-ordinary singularities

  title={A polyhedral characterization of quasi-ordinary singularities},
  author={Hussein Mourtada and Bernd Schober},
  journal={arXiv: Algebraic Geometry},
Given an irreducible hypersurface singularity of dimension $d$ (defined by a polynomial $f\in K[[ {\bf x} ]][z]$) and the projection to the affine space defined by $K[[ {\bf x} ]]$, we construct an invariant which detects whether the singularity is quasi-ordinary with respect to the projection. The construction uses a weighted version of Hironaka's characteristic polyhedron and successive embeddings of the singularity in affine spaces of higher dimensions. When $ f $ is quasi-ordinary, our… Expand
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