Let $X$ be a canonically polarized variety with hilbert polynomial $h$.
Does there exist a nonrigid canonically polarized varietz with hilbert polynomial $h$?
When is this the case, and when is this not the case?
Let $X$ be a canonically polarized variety with hilbert polynomial $h$. Does there exist a nonrigid canonically polarized varietz with hilbert polynomial $h$? When is this the case, and when is this not the case? 

