Invariants of Newton non-degenerate surface singularities

TL;DR

This paper demonstrates that for certain surface singularities, the link uniquely determines key topological and analytical invariants, confirming a version of Zariski's Conjecture about multiplicity.

Contribution

It shows that the link of a Newton non-degenerate surface singularity determines the Newton diagram, topological type, Milnor fibration, and multiplicity, strengthening the understanding of singularity invariants.

Findings

The Newton diagram can be recovered from the link.

The link determines the embedded topological type.

The link determines the multiplicity of the singularity.

Abstract

We recover the Newton diagram (modulo a natural ambiguity) from the link for any surface hypersurface singularity with non-degenerate Newton principal part whose link is a rational homology sphere. As a corollary, we show that the link determines the embedded topological type, the Milnor fibration, and the multiplicity of such a germ. This proves (even a stronger version of) Zariski's Conjecture about the multiplicity for such a singularity.