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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.16552 |
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| _version_ | 1866909692245049344 |
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| author | Aroca, Fuensanta Ayala, Annel Ilardi, Giovanna |
| author_facet | Aroca, Fuensanta Ayala, Annel Ilardi, Giovanna |
| contents | For an arbitrary hypersurface singularity, we construct a family of semigroups associated with algebraically closed fields that arise as an infinite union of rings of series. These semigroups extend the value semigroup of a plane curve studied by Abhyankar and Moh. The algebraically closed fields under consideration possess a natural valuation that induces a corresponding value semigroup. We establish the necessary conditions under which these semigroups are independent of the choice of the root. Moreover, the extensions proposed by P. González and Kiyek-Micus, where González specifically addresses the case of quasi-ordinary singularities, and the extension introduced by Abbas-Assi, can be understood as particular instances within our constructed family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16552 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Abhyankar-Moh Semigroups for arbitrary hypersurfaces Aroca, Fuensanta Ayala, Annel Ilardi, Giovanna Algebraic Geometry For an arbitrary hypersurface singularity, we construct a family of semigroups associated with algebraically closed fields that arise as an infinite union of rings of series. These semigroups extend the value semigroup of a plane curve studied by Abhyankar and Moh. The algebraically closed fields under consideration possess a natural valuation that induces a corresponding value semigroup. We establish the necessary conditions under which these semigroups are independent of the choice of the root. Moreover, the extensions proposed by P. González and Kiyek-Micus, where González specifically addresses the case of quasi-ordinary singularities, and the extension introduced by Abbas-Assi, can be understood as particular instances within our constructed family. |
| title | Abhyankar-Moh Semigroups for arbitrary hypersurfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2501.16552 |