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Links of sandwiched surface singularities and self-similarity

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Abstract

We characterize sandwiched singularities in terms of their link in two different settings. We first prove that such singularities are precisely the normal surface singularities having self-similar non-archimedean links. We describe this self-similarity both in terms of Berkovich analytic geometry and of the combinatorics of weighted dual graphs. We then show that a complex surface singularity is sandwiched if and only if its complex link can be embedded in a Kato surface in such a way that its complement remains connected.

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Acknowledgements

We would like to warmly thank B. Teissier, who asked us about a characterization of singularities having self-similar Riemann-Zariski spaces. This paper is a tentative answer to his question in the framework of normalized Berkovich analytic spaces. We also thank the referee for their very careful reading of a first version of this paper and for their constructive comments.

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Authors and Affiliations

  1. Institut de Mathématiques de Marseille, Université Aix-Marseille, 13453, Marseille, France

    Lorenzo Fantini

  2. CNRS - Centre de Mathématiques Laurent Schwartz, École polytechnique, 91128, Palaiseau Cedex, France

    Charles Favre

  3. Institut Mathématique de Jussieu, Université Paris Diderot - Université de Paris, Bâtiment Sophie Germain, Place Aurélie Nemours, 75013, Paris Cedex 13, France

    Matteo Ruggiero

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  1. Lorenzo Fantini
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  2. Charles Favre
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  3. Matteo Ruggiero
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Correspondence to Matteo Ruggiero.

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During the preparation of this article the first and the second authors have been supported by the ERC-starting grant project “Nonarcomp” (grant number 307856), and the second author by the ANR project “Défigéo”.

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Fantini, L., Favre, C. & Ruggiero, M. Links of sandwiched surface singularities and self-similarity. manuscripta math. 162, 23–65 (2020). https://doi.org/10.1007/s00229-019-01126-9

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  • DOI: https://doi.org/10.1007/s00229-019-01126-9

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