On exceptional quotient singularities

Cheltsov, Ivan¹ ; Shramov, Constantin²

¹ School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Mayfield Road, Edinburgh, EH93JZ, UK, Laboratory of Algebraic Geometry, GU-HSE, 7 Vavilova street, Moscow 117312, Russia
² Steklov Institute of Mathematics, 8 Gubkina street, Moscow, 119991, Russia, Laboratory of Algebraic Geometry, GU-HSE, 7 Vavilova street, Moscow 117312, Russia

Geometry & topology, Tome 15 (2011) no. 4, pp. 1843-1882.

Résumé

We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the $\alpha$–invariant of Tian, and utilize it to classify four-dimensional and five-dimensional exceptional quotient singularities.

Détail

DOI : 10.2140/gt.2011.15.1843

Keywords: quotient singularities, log canonical threshold, alpha invariant, Fano, group, Kähler–Einstein metric

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