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Irreducibility of analytic arc-sections of hypersurface singularities

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Abstract

We explore the existence of irreducible and reducible arc-sections in an irreducible hypersurface singularity germ along finite projections. In particular we provide examples of irreducible isolated hypersurface singularities for which no irreducible arc-sections exist, and show that reducible ones always exist. Moreover, we give an algorithm to check if a given projection allows irreducible arc-sections, and find them if they exist.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Zaragoza, C/ Pedro Cerbuna 12, 50003, Zaragoza, Spain

    Miguel Angel Marco-Buzunariz

  2. Departamento de Álgebra, Geometría y Topología and Instituto de Matemática Interdisciplinar, Facultad de Ciencias Matemáticas- UCM, Ciudad Universitaria, Plaza de Ciencias, 3, 28040, Madrid, Spain

    Maria Pe Pereira

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  1. Miguel Angel Marco-Buzunariz
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  2. Maria Pe Pereira
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Correspondence to Miguel Angel Marco-Buzunariz.

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M. A. Marco-Buzunariz: Partially supported by MTM2016-76868-C2-2-P and Grupo “Investigación en Educación Matemática” of Gobierno de Aragón/Fondo Social Europeo. M. P. Pereira: Partially supported by MTM2017-89420-P, MTM2016-76868-C2-1-P and ERC Consolidator Grant NMST.

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Marco-Buzunariz, M.A., Pe Pereira, M. Irreducibility of analytic arc-sections of hypersurface singularities. Period Math Hung 82, 136–148 (2021). https://doi.org/10.1007/s10998-020-00346-x

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  • DOI: https://doi.org/10.1007/s10998-020-00346-x

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