On the Griffiths numbers for higher dimensional singularities
Annales de l'Institut Fourier, Volume 65 (2015) no. 1, pp. 389-395.

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.

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.

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, singularités de Gorenstein rigides, singularités irrégulières

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

[1] Anno, R. E. Four-dimensional terminal Gorenstein quotient singularities, Mat. Zametki, Volume 73 (2003) no. 6, pp. 813-820 | DOI | MR | Zbl

[2] Griffiths, Phillip A. Variations on a theorem of Abel, Invent. Math., Volume 35 (1976), pp. 321-390 | DOI | MR | Zbl

[3] Miller, G. A.; Blichfeldt, H. F.; Dickson, L. E. Theory and applications of finite groups, Dover Publications, Inc., New York, 1961, pp. xvii+390 | MR | Zbl

[4] Schlessinger, Michael Rigidity of quotient singularities, Invent. Math., Volume 14 (1971), pp. 17-26 | DOI | MR | Zbl

[5] Siu, Yum-tong Analytic sheaves of local cohomology, Trans. Amer. Math. Soc., Volume 148 (1970), pp. 347-366 | DOI | MR | Zbl

[6] van Straten, D.; Steenbrink, J. Extendability of holomorphic differential forms near isolated hypersurface singularities, Abh. Math. Sem. Univ. Hamburg, Volume 55 (1985), pp. 97-110 | DOI | MR | Zbl

[7] Yau, Stephen S. T. Existence of L 2 -integrable holomorphic forms and lower estimates of T V 1 , Duke Math. J., Volume 48 (1981) no. 3, pp. 537-547 http://projecteuclid.org/euclid.dmj/1077314780 | DOI | MR | Zbl

[8] Yau, Stephen S. T. Various numerical invariants for isolated singularities, Amer. J. Math., Volume 104 (1982) no. 5, pp. 1063-1100 | DOI | MR | Zbl

[9] Yau, Stephen S.-T.; Yu, Yung Gorenstein quotient singularities in dimension three, Mem. Amer. Math. Soc., Volume 105 (1993) no. 505, pp. viii+88 | DOI | MR | Zbl

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