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arXiv · 2604.03164

Lipschitz saturation of toric singularities in any dimension

François Bernard·Enrique Chávez-Martínez·Arturo E. Giles Flores
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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.

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François Bernard, Enrique Chávez-Martínez, Arturo E. Giles Flores. 2026-04-03. Lipschitz saturation of toric singularities in any dimension. https://arxiv.org/abs/2604.03164

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