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Families of curves and alterations. (English) Zbl 0868.14012
Summary: 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 than the author’s previous results [ “Smoothness, semi-stability and alterations”, Publ. Math., Inst. Hautes Étud. Sci. 83, 51-93 (1996)]. In addition we deal with situations where a finite group acts.

MSC:
14H10 Families, moduli of curves (algebraic)
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References:
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