Links of sandwiched surface singularities and self-similarity

  • Lorenzo Fantini
  • Charles Favre
  • Matteo RuggieroEmail author


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.

Mathematics Subject Classification

14B05 32P05 32S05 



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. 1.Institut de Mathématiques de MarseilleUniversité Aix-MarseilleMarseilleFrance
  2. 2.CNRS - Centre de Mathématiques Laurent Schwartz, École polytechniquePalaiseau CedexFrance
  3. 3.Institut Mathématique de JussieuUniversité Paris Diderot - Université de ParisParis Cedex 13France

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