# Hypersurface singularities and virtually overtwisted contact structures

## TL;DR

This paper investigates which lens spaces with contact structures can be realized as boundaries of Milnor fibers of complex hypersurface singularities, establishing necessary conditions for such realizations.

## Contribution

It introduces necessary conditions for realizing lens spaces with contact structures as boundaries of hypersurface singularities, expanding understanding of their geometric and topological properties.

## Key findings

- Identifies conditions under which lens spaces can be boundary of Milnor fibers
- Provides criteria for the existence of virtually overtwisted contact structures
- Enhances classification of hypersurface singularities and their links

## Abstract

It is known that the lens space $L(2n,1)$ supports a virtually overtwisted contact structure arising as the boundary of the Milnor fiber of a complex hypersurface singularity. In this article we study the problem of realizing other $(L(p,q),\xi)$ in such a way, obtaining a series of necessary conditions for this to happen.