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THREE-DIMENSIONAL ISOLATED QUOTIENT SINGULARITIES IN EVEN CHARACTERISTIC

Part of: General commutative ring theory Algebraic groups

Published online by Cambridge University Press:  30 October 2017

VLADIMIR SHCHIGOLEV  and
DMITRY STEPANOV
VLADIMIR SHCHIGOLEV
Affiliation:
Financial University under the Government of the Russian Federation, 49 Leningradsky Prospekt, Moscow, Russia e-mail: shchigolev_vladimir@yahoo.com
DMITRY STEPANOV
Affiliation:
The Department of Mathematical Modelling Bauman Moscow State Technical University 2-ya Baumanskaya ul. 5, Moscow 105005, Russia e-mail: dstepanov@bmstu.ru
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Abstract

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This paper is a complement to the work of the second author on modular quotient singularities in odd characteristic. Here, we prove that if V is a three-dimensional vector space over a field of characteristic 2 and G < GL(V) is a finite subgroup generated by pseudoreflections and possessing a two-dimensional invariant subspace W such that the restriction of G to W is isomorphic to the group SL2(𝔽2n), then the quotient V/G is non-singular. This, together with earlier known results on modular quotient singularities, implies first that a theorem of Kemper and Malle on irreducible groups generated by pseudoreflections generalizes to reducible groups in dimension three, and, second, that the classification of three-dimensional isolated singularities that are quotients of a vector space by a linear finite group reduces to Vincent's classification of non-modular isolated quotient singularities.

MSC classification

Primary: 13A50: Actions of groups on commutative rings; invariant theory
Secondary: 14L30: Group actions on varieties or schemes (quotients)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 2 , May 2018 , pp. 435 - 445
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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