no. 1
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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.2935
Classification: 32S05,  14B05
Keywords: Griffiths number, Hironaka number, rigid Gorenstein singularity, irregular singularity 
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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, Tome 73 (2003) no. 6, pp. 813-820 | Article | MR: 2010650 | Zbl: 1059.14003

[2] Griffiths, Phillip A. Variations on a theorem of Abel, Invent. Math., Tome 35 (1976), pp. 321-390 | Article | MR: 435074 | Zbl: 0339.14003

[3] Miller, G. A.; Blichfeldt, H. F.; Dickson, L. E. Theory and applications of finite groups, Dover Publications, Inc., New York, 1961, xvii+390 pages | MR: 123600 | Zbl: 0098.25103

[4] Schlessinger, Michael Rigidity of quotient singularities, Invent. Math., Tome 14 (1971), pp. 17-26 | Article | MR: 292830 | Zbl: 0232.14005

[5] Siu, Yum-tong Analytic sheaves of local cohomology, Trans. Amer. Math. Soc., Tome 148 (1970), pp. 347-366 | Article | MR: 257403 | Zbl: 0195.36802

[6] van Straten, D.; Steenbrink, J. Extendability of holomorphic differential forms near isolated hypersurface singularities, Abh. Math. Sem. Univ. Hamburg, Tome 55 (1985), pp. 97-110 | Article | MR: 831521 | Zbl: 0584.32018

[7] Yau, Stephen S. T. Existence of L 2 -integrable holomorphic forms and lower estimates of T V 1 , Duke Math. J., Tome 48 (1981) no. 3, pp. 537-547 http://projecteuclid.org/euclid.dmj/1077314780 | Article | MR: 630584 | Zbl: 0474.14020

[8] Yau, Stephen S. T. Various numerical invariants for isolated singularities, Amer. J. Math., Tome 104 (1982) no. 5, pp. 1063-1100 | Article | MR: 675310 | Zbl: 0523.14002

[9] Yau, Stephen S.-T.; Yu, Yung Gorenstein quotient singularities in dimension three, Mem. Amer. Math. Soc., Tome 105 (1993) no. 505, viii+88 pages | Article | MR: 1169227 | Zbl: 0799.14001

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