Lipschitz saturation of toric singularities in any dimension
Algebraic Geometry
2026-04-06 v1 Commutative Algebra
Abstract
We describe the semigroup of the Lipschitz saturation of a complex analytic toric singularity in arbitrary dimension. We give a necessary and sufficient condition for a monomial in the normalization to belong to the Lipschitz saturation, in terms of Newton polyhedra and lattice conditions, and deduce a finite algorithm to compute it. We also show that, in dimension greater than two, Campillo's notion of presaturation differs from the Lipschitz saturation, even for complex singularities.
Keywords
Cite
@article{arxiv.2604.03164,
title = {Lipschitz saturation of toric singularities in any dimension},
author = {François Bernard and Enrique Chávez-Martínez and Arturo E. Giles Flores},
journal= {arXiv preprint arXiv:2604.03164},
year = {2026}
}