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?
The central fiber can even be everywhere non-reduced. This can happen when you take the central fiber of the global image of a global map whose general fiber map is the canonical embedding of a surface of general type with very ample canonical map but its central fiber map is the canonical map of a surface of general type whose canonical map is a double covering onto some rational surface.