[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.
Accepté le :
Publié le :
@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 = {https://www.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 - https://www.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 https://www.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. https://www.numdam.org/articles/10.1016/S1631-073X(02)02273-2/
[1] Toric varieties and toric resolutions, Resolution of Singularities, Progr. Math., 181, Birkhäuser, 2000, pp. 259-283
[2] Combinatorial Convexity and Algebraic Geometry, Springer-Verlag, 1996
[3] Introduction to Toric Varieties, Ann. of Math. Stud., 131, Princeton University Press, 1993
[4] Resolving singularities of plane analytic branches with one toric morphism, Resolution of Singularities, Progr. Math., 181, Birkhäuser, 2000, pp. 315-340
[5] P.D. González Pérez, Toric embedded resolutions of quasi-ordinary hypersurfaces, Preprint, 2001
[6] Toroidal Embeddings, Springer Lecture Notes in Math., 339, Springer-Verlag, 1973
[7] Arcs and wedges on sandwiched surface singularities, Amer. J. Math., Volume 121 (1999) no. 6, pp. 1191-1213
[8] Convex Bodies and Algebraic Geometry, Ann. of Math. Stud., 131, Springer-Verlag, 1988
[9] Gröbner Bases and Convex Polytopes, University Lecture Series, 8, American Mathematical Society, 1996
[10] B. Teissier, Valuations, deformations and toric geometry, in preparation
- Desingularization of binomial varieties using toric Artin stacks, Mathematische Zeitschrift, Volume 306 (2024) no. 3 | DOI:10.1007/s00209-024-03441-8
- Some Ideas in Need of Clarification in Resolution of Singularities and the Geometry of Discriminants, Mathematics Going Forward, Volume 2313 (2023), p. 29 | DOI:10.1007/978-3-031-12244-6_3
- Functorial resolution except for toroidal locus. Toroidal compactification, Advances in Mathematics, Volume 407 (2022), p. 108551 | DOI:10.1016/j.aim.2022.108551
- Partial resolution by toroidal blow-ups, Tunisian Journal of Mathematics, Volume 1 (2019) no. 1, p. 3 | DOI:10.2140/tunis.2019.1.3
- Valuations on Equicharacteristic Complete Noetherian Local Domains, Extended Abstracts February 2016, Volume 9 (2018), p. 39 | DOI:10.1007/978-3-030-00027-1_6
- A procedure for computing the log canonical threshold of a binomial ideal, manuscripta mathematica, Volume 155 (2018) no. 1-2, p. 141 | DOI:10.1007/s00229-017-0929-4
- A short note on the multiplier ideals of monomial space curves, Journal of Pure and Applied Algebra, Volume 220 (2016) no. 6, p. 2459 | DOI:10.1016/j.jpaa.2015.11.017
- Multiplier ideals of monomial space curves, Proceedings of the American Mathematical Society, Series B, Volume 1 (2014) no. 4, p. 33 | DOI:10.1090/s2330-1511-2014-00001-8
- Desingularization of binomial varieties in arbitrary characteristic. Part I. A new resolution function and their properties, Mathematische Nachrichten, Volume 285 (2012) no. 11-12, p. 1316 | DOI:10.1002/mana.201100108
- Embedded desingularization of toric varieties, Journal of Symbolic Computation, Volume 46 (2011) no. 11, p. 1229 | DOI:10.1016/j.jsc.2011.08.005
- A New Desingularization Algorithm for Binomial Varieties in Arbitrary Characteristic, Mathematical Software – ICMS 2010, Volume 6327 (2010), p. 217 | DOI:10.1007/978-3-642-15582-6_38
- Desingularization of toric and binomial varieties, Journal of Algebraic Geometry, Volume 15 (2006) no. 3, p. 443 | DOI:10.1090/s1056-3911-06-00430-9
Cité par 12 documents. Sources : Crossref
