[Résolution plongée d'une variété torique non nécessairement normale]
Nous présentons une méthode de construction d'une résolution plongée partielle d'une variété torique affine non nécessairement normale ZΓ plongée de manière équivariante dans une variété torique affine normale Zρ. Cette résolution partielle est une normalisation plongée de ZΓ dans un espace ambiant torique normal et une résolution des singularités de l'espace ambiant, qui existe toujours, fournit une résolution plongée des singularités. L'avantage est que cette résolution partielle est entièrement déterminée par le plongement ZΓ⊂Zρ. Une conséquence est la construction de la normalisation sans calcul de la saturation du semigroupe Γ de la variété torique (voir [3]). Ce résultat est valide sur un corps k algébriquement clos de caractéristique quelconque.
We give a method to construct a partial embedded resolution of a nonnecessarily normal affine toric variety ZΓ equivariantly embedded in a normal affine toric variety Zρ. This partial resolution is an embedded normalization inside a normal toric ambient space and a resolution of singularities of the ambient space, which always exists, provides an embedded resolution. The advantage is that this partial resolution is completely determined by the embedding ZΓ⊂Zρ. As a by-product, the construction of the normalization is made without an explicit computation of the saturation of the semigroup Γ of the toric variety (see [3]). This result is valid for a base field k algebraically closed of arbitrary characteristic.
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@article{CRMATH_2002__334_5_379_0,
author = {Gonz\'alez P\'erez, Pedro Daniel and Teissier, Bernard},
title = {Embedded resolutions of non necessarily normal affine toric varieties},
journal = {Comptes Rendus. Math\'ematique},
pages = {379--382},
publisher = {Elsevier},
volume = {334},
number = {5},
year = {2002},
doi = {10.1016/S1631-073X(02)02273-2},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02273-2/}
}
TY - JOUR AU - González Pérez, Pedro Daniel AU - Teissier, Bernard TI - Embedded resolutions of non necessarily normal affine toric varieties JO - Comptes Rendus. Mathématique PY - 2002 SP - 379 EP - 382 VL - 334 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02273-2/ DO - 10.1016/S1631-073X(02)02273-2 LA - en ID - CRMATH_2002__334_5_379_0 ER -
%0 Journal Article %A González Pérez, Pedro Daniel %A Teissier, Bernard %T Embedded resolutions of non necessarily normal affine toric varieties %J Comptes Rendus. Mathématique %D 2002 %P 379-382 %V 334 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02273-2/ %R 10.1016/S1631-073X(02)02273-2 %G en %F CRMATH_2002__334_5_379_0
González Pérez, Pedro Daniel; Teissier, Bernard. Embedded resolutions of non necessarily normal affine toric varieties. Comptes Rendus. Mathématique, Tome 334 (2002) no. 5, pp. 379-382. doi : 10.1016/S1631-073X(02)02273-2. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02273-2/
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