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Contact loci and Hironaka’s order

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Abstract

We study contact loci sets of arcs and the behavior of Hironaka’s order function defined in constructive Resolution of singularities. We show that this function can be read in terms of the irreducible components of the contact loci sets at a singular point of an algebraic variety.

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Acknowledgements

We profited from conversations with C. Abad, A. Benito and O. E. Villamayor. We would like to thank S. Ishii and T. Yasuda for useful comments. Finally, we also want to thank the referee for careful reading and useful suggestions.

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Author notes

  1. B. Pascual-Escudero

    Present address: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2200, Copenhagen, Denmark

Authors and Affiliations

  1. Depto. Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid and Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Canto Blanco, 28049, Madrid, Spain

    A. Bravo

  2. Depto. Matemática Aplicada, and IMUVA, Instituto de Matemáticas, Universidad de Valladolid, Valladolid, Spain

    S. Encinas

  3. Laboratoire des Sciences du Numérique de Nantes - Centrale Nantes, Nantes, France

    B. Pascual-Escudero

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  1. A. Bravo
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Correspondence to S. Encinas.

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The authors were partially supported by MTM2015-68524-P; The first author was partially supported from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa” Programme for Centres of Excellence in R&D (SEV-2015-0554).

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Bravo, A., Encinas, S. & Pascual-Escudero, B. Contact loci and Hironaka’s order. manuscripta math. 166, 131–165 (2021). https://doi.org/10.1007/s00229-020-01235-w

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  • DOI: https://doi.org/10.1007/s00229-020-01235-w

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