Geodesic
On the classification of singularities that are equivariant simple with respect to representations of cyclic groups
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 2, pp. 155-159 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of classification of function germs $(\mathbb{C}^n, 0)\to(\mathbb{C}, 0)$ that are equivariant simple with respect to various representations of a finite cyclic group $\mathbb{Z}_m$, $m\ge3$, on $\mathbb{C}^n$ and $\mathbb{C}$ up to equivariant automorphisms of $\mathbb{C}^n$. In the case of matching scalar actions of the group it is shown that for $n\ge2$ there exist no equivariant simple function germs. This result is generalized to the cases where the group action in several variables in $\mathbb{C}^n$ coincides with the action of the group on $\mathbb{C}$. In addition, it is shown that in the case of non-matching scalar actions of $\mathbb{Z}_3$ on $\mathbb{C}^2$ and on $\mathbb{C}$ any equivariant simple function germ is equivalent to one of the germs $A_{3k+1}$, $k\in\mathbb{Z}_{\ge0}$.
Keywords: classification of singularities, simple singularities, equivariant functions.
Mots-clés : group action 
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E. A. Astashov. On the classification of singularities that are equivariant simple with respect to representations of cyclic groups. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 2, pp. 155-159. http://geodesic.mathdoc.fr/item/VUU_2016_26_2_a0/

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