Patching local uniformizations

Abstract

Patching local uniformizationsAnnales scientifiques de l'É.N.S. 4 e série, tome 25, n o 6 (1992), p. 629-677 <http://www.numdam.org/item?id=ASENS_1992_4_25_6_629_0> © Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1992, tous droits réservés. L'accès aux archives de la revue « Annales scientifiques de l'É.N.S. » (http://www. elsevier.com/locate/ansens) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

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“…Is there a resolution π : A 3 → A 3 such that this action can be lifted to the resolved X ⊆ A 3 ? The answer to this question is 'yes' and was first given in arbitrary dimension by Villamayor [40]. More precisely, if G acts on X ⊆ A 3 one can find a resolution of X that is a composition of blowups in centers invariant under the action of G. Therefore, 4 One knows for example that a polynomial map ϕ : A n C → A n C is an automorphism if and only if it is bijective; see [23,Lemma II.3.4].…”

Equivariant resolution of points of indeterminacy

“…be the canonical resolution of singularities of X, as in [V,Theorem 7.6.1] or [BM,Theorem 13.2]. Here X l is smooth, the centers C i ⊂ X i are smooth and G-invariant, and the action of G lifts to the entire resolution sequence (1).…”

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“…be the canonical resolution of singularities of X, as in [V,Theorem 7.6.1] or [BM,Theorem 13.2]. Here X l is smooth, the centers C i ⊂ X i are smooth and G-invariant, and the action of G lifts to the entire resolution sequence (1).…”