Geodesic
THREE-DIMENSIONAL ISOLATED QUOTIENT SINGULARITIES IN EVEN CHARACTERISTIC
Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 435-445

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
SHCHIGOLEV, VLADIMIR; STEPANOV, DMITRY. THREE-DIMENSIONAL ISOLATED QUOTIENT SINGULARITIES IN EVEN CHARACTERISTIC. Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 435-445. doi: 10.1017/S0017089517000192
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[1] 1. Benson, D. J., Polynomial invariants of finite groups, London Mathematical Society Lecture Note Series, vol. 190 (Cambridge University Press, Cambridge, UK, 1993). Google Scholar

[2] 2. Bonnafé, C., Representations of SL(𝔽), Algebra and Applications, vol. 13 (Springer Verlag, London, 2011). Google Scholar

[3] 3. Sah, C.-H., Cohomology of split group extensions, II, J. Algebra 45 (1977), 17–68. Google Scholar

[4] 4. Cline, E., Parshall, B. and Scott, L., Cohomology of finite groups of Lie type, I, Publ. Math. l'IHES 45 (1975), 169–191. Google Scholar | DOI

[5] 5. Campbell, H. E. A. E. and Wehlau, D. L., Modular invariant theory, Encyclopaedia of Mathematical Sciences, vol. 139, Invariant Theory and Algebraic Transformation Groups VIII (subseries Gamkrelidze, R. V. and Popov V. L., Editors) (Springer, 2011), XIV, 234 p. Google Scholar

[6] 6. Kemper, G. and Malle, G., The finite irreducible linear groups with polynomial ring of invariants, Transformation Groups 2 (1) (1997), 57–89. Google Scholar | DOI

[7] 7. Stepanov, D. A., Three-dimensional isolated quotient singularities in odd characteristic, Sbornik: Mathematics 207 (6) (2016), 873–887. Google Scholar

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