On the Griffiths numbers for higher dimensional singularities

Du, Rong; Gao, Yun

doi:10.5802/aif.2935

On the Griffiths numbers for higher dimensional singularities
[Sur les nombres de Griffiths pour les singularités de dimension supérieure]

Du, Rong ¹ ; Gao, Yun ²

¹ East China Normal University Department of Mathematics Shanghai Key Laboratory of PMMP Rm. 312, Math. Bldg, No. 500, Dongchuan Road Shanghai, 200241, (P. R. China)
² Shanghai Jiao Tong University Department of Mathematics Shanghai 200240, (P. R. of China)

Annales de l'Institut Fourier, Tome 65 (2015) no. 1, pp. 389-395.

Résumé
Abstract

Nous montrons que la conjecture de Yau sur les inégalités concernant le $(n - 1)$ -ième nombre de Griffiths et le $(n - 1)$ -ième nombre de Hironaka n’est pas vraie en général pour les singularités de Gorenstein isolées rigides de dimension supérieure à 2. Cependant, la première conjecture sur les inégalités concernant le $(n - 1)$ -ième nombre de Griffiths est vraie pour les singularités irrégulières.

We show that Yau’s conjecture on the inequalities for $(n - 1)$ -th Griffiths number and $(n - 1)$ -th Hironaka number does not hold for isolated rigid Gorenstein singularities of dimension greater than 2. But his conjecture on the inequality for $(n - 1)$ -th Griffiths number is true for irregular singularities.

Zbl

DOI : 10.5802/aif.2935

Classification : 32S05, 14B05
Keywords: Griffiths number, Hironaka number, rigid Gorenstein singularity, irregular singularity
Mot clés : nombre de Griffiths, nombre de Hironaka, singularitÃ©s de Gorenstein rigides, singularitÃ©s irrÃ©guliÃ¨res

Affiliations des auteurs :

Du, Rong ¹ ; Gao, Yun ²

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Du, Rong; Gao, Yun. On the Griffiths numbers for higher dimensional singularities. Annales de l'Institut Fourier, Tome 65 (2015) no. 1, pp. 389-395. doi : 10.5802/aif.2935. http://www.numdam.org/articles/10.5802/aif.2935/

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