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Russia Moscow
Section Mathematics
Title On the classification of singularities that are equivariant simple with respect to representations of cyclic groups
Author(-s) Astashov E.A.a
Affiliations Lomonosov Moscow State Universitya
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 $\mathbb{Z}_m$, $m\geqslant 3$, 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 $n\geqslant 2$ 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 $A_{3k+1}$, $k\in\mathbb{Z}_{\geqslant 0}$.
Keywords classification of singularities, simple singularities, group action, equivariant functions
UDC 512.761.5
MSC 14B05
DOI 10.20537/vm160201
Received 12 May 2016
Language Russian
Citation Astashov E.A. On the classification of singularities that are equivariant simple with respect to representations of cyclic groups, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 2, pp. 155-159.
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