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Regular version of the site

Article

О простых Z3-инвариантных ростках функций

Гусейн-Заде С. М., Раух А. Я.

V.I.Arnold classified simple (i.e. having no moduli for the classification) singularities (function germs) and also simple boundary singularities: function germs invariant with respect to the action
σ(x1;y1,…,yn)=(−x1;y1,…,yn) of the group Z2. In particular, it was shown 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 stable 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 of the authors, there were obtained analogues of the latter statements for function germs invariant with respect to an arbitrary
action of the group Z2 and also for corner singularities. In this paper, we give an analogue of the criterion of simplicity in terms of the intersection form for functions invariant with respect to a number of actions (representations) of the group Z3.