Normalization of Puiseux Hypersurfaces
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912829737533440 |
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| author | Aroca, Fuensanta Ayala, Annel Castañón, Oscar Penagos, Diana Mendez Ochoa, Damián Plénat, Camille |
| author_facet | Aroca, Fuensanta Ayala, Annel Castañón, Oscar Penagos, Diana Mendez Ochoa, Damián Plénat, Camille |
| contents | It is known that the normalization of a quasi-ordinary complex singularity is a Hirzebruch-Jung, see [Gon00; Pop04; AS05]. We extend this result to Puiseux hypersurfaces. Moreover, we prove that Hirzebruch-Jung singularities are precisely normalizations of Puiseux hypersurfaces. Our result holds over an algebraically closed field whose characteristic does not divide the degree of the polynomial defining the hypersurface. Finally, in the analytic complex case, we conclude that the normalization of an irreducible Puiseux hypersurface is the normalization of a complex analytic quasi-ordinary singularity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_15863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normalization of Puiseux Hypersurfaces Aroca, Fuensanta Ayala, Annel Castañón, Oscar Penagos, Diana Mendez Ochoa, Damián Plénat, Camille Algebraic Geometry It is known that the normalization of a quasi-ordinary complex singularity is a Hirzebruch-Jung, see [Gon00; Pop04; AS05]. We extend this result to Puiseux hypersurfaces. Moreover, we prove that Hirzebruch-Jung singularities are precisely normalizations of Puiseux hypersurfaces. Our result holds over an algebraically closed field whose characteristic does not divide the degree of the polynomial defining the hypersurface. Finally, in the analytic complex case, we conclude that the normalization of an irreducible Puiseux hypersurface is the normalization of a complex analytic quasi-ordinary singularity. |
| title | Normalization of Puiseux Hypersurfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2511.15863 |