Existence and maximal corank of simple $Z_p$-invariant germs

TL;DR

This paper refines bounds on the corank of equivariantly stable singularities with prime order symmetry and shows the maximal corank grows logarithmically with the prime.

Contribution

It improves the upper bound on corank and establishes asymptotic growth of maximal corank for simple $ ext{Z}_p$-invariant germs.

Findings

Maximal corank tends to infinity as p increases.

Corank growth is asymptotically logarithmic.

Previous bounds are valid up to order of magnitude.

Abstract

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.