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.

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.