On exceptional quotient singularities

Cheltsov, Ivan; Shramov, Constantin

doi:10.2140/gt.2011.15.1843

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On exceptional quotient singularities

Ivan Cheltsov and Constantin Shramov

Geometry & Topology 15 (2011) 1843–1882

DOI: 10.2140/gt.2011.15.1843

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

Volume 15, issue 4 (2011)