The corank and the index are blow-Nash invariants

Abstract

Is the corank an invariant of the blow-analytic equivalence between real analytic function germs? We give a positive answer in the case of the blow-Nash equivalence, which is a natural variant of the blow-analytic equivalence for Nash function germs. In addition, we prove that the index is also a blow-Nash invariant. Their proof is based on the computation of some virtual Poincaré polynomials and zeta functions associated to a Nash function germ.