Algebraic geometry
2-Jordan blocks for the eigenvalue λ=1 of Yomdin–Lê surface singularities
[2-Blocs de Jordan pour la valeur propre λ=1 des singularités de surface de type Yomdin–Lê]

Présenté par : Claire Voisin

Martín-Morales, Jorge1
1 Centro Universitario de la Defensa – IUMA, Academia General Militar, Ctra. de Huesca s/n, 50090 Zaragoza, Spain
Comptes Rendus. Mathématique, Tome 353 (2015) no. 2, pp. 161-165.

L'objet principal de cet article est de calculer explicitement les blocs de Jordan d'ordre 2 pour la valeur propre λ=1 d'une singularité de surface de type Yomdin–Lê, en fonction des données combinatoires de son cône tangent. Notre méthode s'appuie sur l'utilisation d'une généralisation de la suite spectrale de Steenbrink et d'une certaine résolution torique partielle de cette famille de singularités. La suite spectrale et la résolution partielle ont déjà été développées par l'auteur dans des travaux précédents.

The main purpose of this paper is to explicitly calculate the Jordan blocks of size 2 for the eigenvalue λ=1 of a Yomdin–Lê surface singularity, in terms of the combinatorial data of its tangent cone. Our method relies on the use of a generalization of Steenbrink's spectral sequence and a certain partial toric resolution of this family of singularities. Both the spectral sequence and the partial resolution have already been developed by the author in previous works.

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Accepté le :
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DOI : 10.1016/j.crma.2014.11.006
Martín-Morales, Jorge 1

1 Centro Universitario de la Defensa – IUMA, Academia General Militar, Ctra. de Huesca s/n, 50090 Zaragoza, Spain 
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Martín-Morales, Jorge. 2-Jordan blocks for the eigenvalue $ \lambda =1$ of Yomdin–Lê surface singularities. Comptes Rendus. Mathématique, Tome 353 (2015) no. 2, pp. 161-165. doi : 10.1016/j.crma.2014.11.006. https://www.numdam.org/articles/10.1016/j.crma.2014.11.006/

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  • Martín-Morales, Jorge Semistable reduction of a normal crossing Q Q -divisor, Annali di Matematica Pura ed Applicata (1923 -), Volume 195 (2016) no. 5, p. 1749 | DOI:10.1007/s10231-015-0546-3

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☆ The author is partially supported by the Spanish Ministry of Education MTM2010-21740-C02-02, E15 Grupo Consolidado Geometría from the Gobierno de Aragón, FQM-333 from Junta de Andalucía, and PRI-AIBDE-2011-0986 Acción Integrada Hispano-Alemana.