I have a family of deformation $\mathcal{X}\to B$ of a surface $S$. The surface has a finite number of singular point and it is normal. There is a divisor $D\subset B$ such that the surface $\mathcal{X}_b$ is smooth and of general type for $b\notin D$. I think that Hironaka's desingularization of $S$ should be of general type too. It is true?
For example, is it true that the deformation of the desingularization is the desingularization of the deformation? This would resolve my problem, as the deformation of a surface of general type results again in a surface of general type, and the resolution of a smooth surface is the same surface.
Thank you!