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On exceptional quotient singularities

Ivan Cheltsov and Constantin Shramov

Geometry & Topology 15 (2011) 1843–1882
Abstract

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

Keywords
quotient singularities, log canonical threshold, alpha invariant, Fano, group, Kähler–Einstein metric
References
Publication
Received: 28 October 2009
Revised: 20 June 2011
Accepted: 7 September 2011
Published: 14 October 2011
Proposed: Gang Tian
Seconded: Simon Donaldson, Richard Thomas
Authors
Ivan Cheltsov
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
http://www.maths.ed.ac.uk/cheltsov/
Constantin Shramov
Steklov Institute of Mathematics
8 Gubkina street
Moscow
119991
Russia
Laboratory of Algebraic Geometry
GU-HSE
7 Vavilova street
Moscow 117312
Russia