On the smoothings of non-normal isolated surface singularities

TL;DR

This paper explores how non-normal isolated surface singularities can have Milnor fibers that differ from their normalizations, impacting the understanding of Stein fillings of singularity links.

Contribution

It demonstrates that non-normal singularities can produce distinct Milnor fibers, expanding the known diversity of Stein fillings for normal isolated singularities.

Findings

Non-normal singularities can have non-diffeomorphic Milnor fibers.

Non-normal singularities enrich the set of Stein fillings.

Open questions remain about the relationship between normal and non-normal singularities.

Abstract

We show that isolated surface singularities which are non-normal may have Milnor fibers which are non-diffeomorphic to those of their normalizations. Therefore, non-normal isolated singularities enrich the collection of Stein fillings of links of normal isolated singularities. We conclude with a list of open questions related to this theme.