Lipschitz saturation of toric singularities in any dimension
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915913425485824 |
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| author | Bernard, François Chávez-Martínez, Enrique Flores, Arturo E. Giles |
| author_facet | Bernard, François Chávez-Martínez, Enrique Flores, Arturo E. Giles |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03164 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lipschitz saturation of toric singularities in any dimension Bernard, François Chávez-Martínez, Enrique Flores, Arturo E. Giles Algebraic Geometry Commutative Algebra 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. |
| title | Lipschitz saturation of toric singularities in any dimension |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2604.03164 |