Let $f : X \rightarrow S$ be a morphism between schemes, with $f$ locally of finite presentation, proper and flat, and $S$ the spectrum of a discrete valuation ring with closed point $s$.
Assume that the special fiber $X_s$ is smooth. Is the generic fiber smooth?
In other words: is it impossible to have a flat (algebraic) family of proper singular varieties degenerating into a smooth variety?
Some questions with similar flavour:
If the reduction is smooth and projective, can I conclude the same about the scheme
How to understand a fibre over a generic point?
When is the canonical model of a curve nonsingular
Smoothness of the total space of a family of curves