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This article is cited in 6 scientific papers (total in 6 papers)
MATHEMATICS
On the classification of singularities that are equivariant simple with respect to representations of cyclic groups
E. A. Astashov Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory, 1, GSP-1, Moscow, 119991, Russia
Abstract:
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, group action, equivariant functions.
Received: 12.05.2016
Citation:
E. A. Astashov, “On the classification of singularities that are equivariant simple with respect to representations of cyclic groups”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:2 (2016), 155–159
Linking options:
https://www.mathnet.ru/eng/vuu526 https://www.mathnet.ru/eng/vuu/v26/i2/p155
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