Let $X$ be a finite type scheme over $\mathbb{C}$ and let $ \mathcal{X} \to Spec(\mathbb{C}[[x]])$ be a formal deformation of $X$ (flat family with special fiber $X$). Which of the following assumptions (or combinations thereof) are sufficient to imply that this deformation is convergent? (i.e. that it is the pullback of some flat finite type analytic space $\tilde{\mathcal{X}} \to Spec(\mathbb{C}\{x\})$).
$X$ quasi-projective.
$X$ proper.
$X$ projective (equivalently, both (1) and (2)).
$X$ affine.
$X$ smooth.
Are there simple (preferably low dimensional) counter examples to convergence of formal defomrations?