Characteristic polyhedra of singularities without completion: part II

Cossart, Vincent ^[1] ; Schober, Bernd ^[2]
1. [1] Laboratoire de Mathémathiques de Versailles CNRS UMR 8100, Université Paris-Saclay, 45 avenue des États-Unis, 78035, Versaills Cedex, France
2. [2] Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 2, 2021, págs. 351-392
Idioma: inglés
DOI: 10.1007/s13348-020-00291-5
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Resumen
- 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.