# Links of sandwiched surface singularities and self-similarity

## TL;DR

This paper characterizes sandwiched surface singularities through their links, demonstrating their self-similarity in non-archimedean and complex geometric settings, and linking these properties to embeddings in Kato surfaces.

## Contribution

It provides a new characterization of sandwiched singularities via self-similar non-archimedean links and their embeddings in complex surfaces, connecting geometric and combinatorial perspectives.

## Key findings

- Sandwiched singularities have self-similar non-archimedean links.
- Such singularities can be characterized by their complex links embedding in Kato surfaces.
- The paper links combinatorial dual graph properties with analytic geometry.

## 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.