ON THE CLASSIFICATION OF FUNCTION GERMS OF TWO VARIABLES THAT ARE EQUIVARIANT SIMPLE WITH RESPECT TO AN ACTION OF THE CYCLIC GROUP OF ORDER THREE
- Authors: Astashov E.A.1
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Affiliations:
- post-graduate student, Lomonosov Moscow State University, Leninskie Gory 1, GSP-1, Moscow, 119991, Russia.
- Issue: Vol 22, No 3-4 (2016)
- Pages: 7-13
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/4252
- DOI: https://doi.org/10.18287/2541-7525-2016-22-3-4-7-13
- ID: 4252
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Abstract
We consider the problem to classify function germs (C2 , 0) → (C, 0), that are equivariant simple with respect to nontrivial actions of the group Z3 on C2 and on C up to equivariant automorphism germs (C2 , 0) → (C2 , 0). The complete classification of such germs is obtained in the case of nonscalar action of Z3 on C2 that is nontrivial in both coordinates. Namely, a germ is equivariant simple with respect to such a pair of actions if and only if it is equivalent to ine of the following germs:
- (x, y) → x3k+1 + y2 , k ≥ 1;
- (x, y) → x2y + y3k−1 , k ≥ 2;
- (x, y) → x4 + xy3
- (x, y) → x4 + y5 .
About the authors
E. A. Astashov
post-graduate student, LomonosovMoscow State University, Leninskie Gory 1, GSP-1, Moscow, 119991, Russia.
Author for correspondence.
Email: morenov.sv@ssau.ru
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