Contact Singularities

A contact singularity is a normal singularity $(V,0)$ together with a holomorphic contact form $\eta$ on $V\mathrm{\backslash }$ Sing $V$ in a neighbourhood of 0, i.e. $\eta \wedge (d\eta {)}^r$ has no zero, where dim $V=2r+1$. The main result of this paper is that there are no isolated contact singularities.