Suppose I have a one parameter flat family of complex surfaces (regular, of general type) whose general fibre is smooth. Is it possible for the central fibre to have singularities which are not canonical? If so, how bad can they be? 



Singularities of a central fibre of a flat family of smooth surfaces
The cone over a plane curve of degree $d$ deforms to a smooth surface in $\mathbb P^3$ of degree $d$. Take $d\ge 5$ to see that things can be arbitrarily bad.


