Geodesic
Three-dimensional isolated quotient singularities in odd characteristic
Sbornik. Mathematics, Tome 207 (2016) no. 6, pp. 873-887

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Let a finite group $G$ act linearly on a finite-dimensional vector space $V$ over an algebraically closed field $k$ of characteristic $p>2$. Suppose that the quotient space $V/G$ has an isolated singularity only. The isolated singularities of the form $V/G$ are completely classified in the case when $p$ does not divide the order of $G$, and their classification reduces to Vincent's classification of isolated quotient singularities over $\mathbb C$. In the present paper we show that, if $\dim V=3$, then the classification of isolated quotient singularities reduces to Vincent's classification in the modular case as well (when $p$ divides $|G|$). Some remarks on quotient singularities in other dimensions and in even characteristic are also given. Bibliography: 14 titles.
Keywords: quotient singularity, modular representation, pseudo-reflection
Mots-clés : transvection. 
@article{SM_2016_207_6_a5,
     author = {D. A. Stepanov},
     title = {Three-dimensional isolated quotient singularities in odd characteristic},
     journal = {Sbornik. Mathematics},
     pages = {873--887},
     publisher = {mathdoc},
     volume = {207},
     number = {6},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_6_a5/}
}
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D. A. Stepanov. Three-dimensional isolated quotient singularities in odd characteristic. Sbornik. Mathematics, Tome 207 (2016) no. 6, pp. 873-887. http://geodesic.mathdoc.fr/item/SM_2016_207_6_a5/