Hypersurface singularities and virtually overtwisted contact structures

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.