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arXiv · 2511.15863

Normalization of Puiseux Hypersurfaces

Fuensanta Aroca·Annel Ayala·Oscar Castañón·Diana Mendez Penagos·Damián Ochoa·Camille Plénat
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Abstract

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.

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Fuensanta Aroca, Annel Ayala, Oscar Castañón, Diana Mendez Penagos, Damián Ochoa, Camille Plénat. 2025-11-19. Normalization of Puiseux Hypersurfaces. https://arxiv.org/abs/2511.15863

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