FAMILIES OF CURVES AND ALTERATIONS

In this article it is shown that any family of curves can be altered i nto a semistable family. This implies that if S is an excellent scheme of dimension at most 2 and X is a separated integral scheme of finite type over S, then X can be altered into a regular scheme. This result is stronger then the results of [Smoothness, semi-stability and alter ations to appear in Publ. Math. IHES]. In addition we deal with situat ions where a finite group acts.