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Дата последнего поиска статьи во внешних источниках: 20 октября 2021 г.
Аннотация:V.I.Arnold classified simple (i.e., having no moduli for classification) singularities (function germs) and also simple boundary singularities, that is, function germs invariant with respect to the action σ(x1;y1,…,yn)=(−x1;y1,…,yn) of the group Z_2. In particular, he showed that a function germ (a germ of a boundary singularity) is simple if and only if the intersection form (respectively, the restriction of the intersection form to the subspace of anti-invariant cycles) of a germ in 3+4s variables stably equivalent to the one under consideration is negative definite and if and only if the (equivariant) monodromy group on the corresponding space is finite. In a previous paper the authors obtained analogues of the latter statements for function germs invariant with respect to an arbitrary action of the group Z_2 and also for corner singularities. This paper presents an analogue of the simplicity criterion in terms of the intersection form for functions invariant with respect to a number of actions (representations) of the group Z_3.