The stratification associated with the number of generators of the ideals of the punctual Hilbert scheme of points on the affine plane has been studied since the ' 70s.
I will present a formula for the E-polynomials of these strata. The proof uses a Grassmannian bundle structure on the refined Hilbert scheme: a particular flag-type generalization of Hilbert scheme, together with the motivic property of the E-polynomial.
