arXiv subjects
Publications and source records attributed to Ivan Proskurnin.
In this paper we improve the previously achieved upper bound on the corank of an equivariantly stable singularity for a group of prime order. We also prove that the maximal corank of a simple $\mathbb{Z}_p$-invariant germ tends to infinity as $p$ increases and is asymptotically logarithmic, so the previously obtained bound is valid up to order of magnitude.
We prove that equivariantly simple invariant singularities can only exist for very few representations of a group of prime order: for real representations and some ``almost, but not quite real'' representations.
We prove a lower bound for the Milnor number of function germ invariant with respect to a finite abelian group action. It is shown that this bound is tight for functions of arbitrarily many variables. We also prove the function germs that reach this lower bound are equivariantly stable, i.e. invariant analogues of Morse singularities.