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Families of curves and alterations

A. Johan De Jong — 1997

Annales de l'institut Fourier

In this article it is shown that any family of curves can be altered into a semi-stable 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 alterations to appear in Publ. Math. IHES]. In addition we deal with situations where a finite group acts.

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