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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)
##### Keywords:
family of curves; alterations; group actions
Full Text:
##### References:
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