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Let $V$ be a variety over $\mathbb{C}$ and suppose $O$ is a singular point of $V$. Are there conditions on $(V,O)$ such that a versal deformation $W$ of $(V,O)$ has only quasi-ordinary singularities.

In particular, if we assume $(V,O)$ is a plane curve singularity (or, more generally, a quasi-ordinary singularity), then is there some condition which will force a versal deformation $W$ of $V$ to have quasi-ordinary singularities?

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    $\begingroup$ Infinitesimal deformations of isolated plane curve singularities, or more generally of isolated local complete intersection singularities, are unobstructed. Thus, every hull is formally smooth. $\endgroup$
    – Jason Starr
    Commented Oct 11, 2015 at 23:01

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