The Chow of S (inverted right perpendicular n inverted left perpendicular) and the universal subscheme

Abstract

We prove that any element in the Chow ring of the Hilbert scheme Hilbn of n points on a smooth surface S is a universal class, i.e. the push-forward of a polynomial in the Chern classes of the universal subschemes on Hilb[subscript n] x S[superscript K] for some k ∈N, with coefficients pulled back from the Chow of S[superscript K].