Families of curves and alterations
Annales de l'Institut Fourier, Volume 47 (1997) no. 2, p. 599-621
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.
Dans l’article on prouve que toute famille de courbes peut être altérée en une famille semi-stable. Soit S un schéma excellent de dimension 0, 1 ou 2 et soit X un schéma séparé de type fini sur S. Alors le résultat implique qu’on peut altérer X en un schéma régulier. C’est un résultat plus fort que ceux de [Smoothness, semi-stability and alterations à paraître dans Publ. Math. IHES]. De plus, on considère des situations où un groupe fini agit, et on obtient des résultats analogues.
@article{AIF_1997__47_2_599_0,
     author = {Jong, A. Johan de},
     title = {Families of curves and alterations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {47},
     number = {2},
     year = {1997},
     pages = {599-621},
     doi = {10.5802/aif.1575},
     zbl = {0868.14012},
     mrnumber = {98f:14019},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1997__47_2_599_0}
}
Jong, A. Johan de. Families of curves and alterations. Annales de l'Institut Fourier, Volume 47 (1997) no. 2, pp. 599-621. doi : 10.5802/aif.1575. http://www.numdam.org/item/AIF_1997__47_2_599_0/

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