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Journal Articles Collectanea Mathematica Year : 2020

Characteristic polyhedra of singularities without completion: part II

Abstract

Hironaka's characteristic polyhedron is an important combinatorial object reflecting the local nature of a singularity. We prove that it can be determined without passing to the completion if the local ring is a G-ring and if additionally either it is Henselian, or a certain polynomiality condition (Pol) holds, or a mild condition (*) on the singularity holds. For example, the latter is fulfilled if the residue field is perfect.
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hal-04439582 , version 1 (05-02-2024)
hal-04439582 , version 2 (08-02-2024)

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Vincent Cossart, Bernd Schober. Characteristic polyhedra of singularities without completion: part II. Collectanea Mathematica, 2020, 72, pp.351 - 392. ⟨10.1007/s13348-020-00291-5⟩. ⟨hal-04439582v2⟩
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