Abstract
In Hironaka (J. Math. Kyoto Univ. 7(3):251–293, 1967) defines characteristic polyhedra of a singularity embedded in Spec(R), where R is a regular local ring. Unfortunately, to build these polyhedra, he must pick up coordinates in the completion \(\widehat{R}\). In this article, we show that, in the hypersurface case, whenever R is a G-ring, by using a different algorithm than Hironaka’s, it is not necessary to extend R to compute the polyhedra.
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Dedicated to Heisuke Hironaka on his eightieth birthday.
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Cossart, V., Piltant, O. Characteristic polyhedra of singularities without completion. Math. Ann. 361, 157–167 (2015). https://doi.org/10.1007/s00208-014-1064-0
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DOI: https://doi.org/10.1007/s00208-014-1064-0