The asymptotic profile of χy-genera of Hilbert schemes of points on K3 surfaces

The Hodge numbers of the Hilbert schemes of points on algebraic surfaces are given by Gottsche's formula, which expresses the generating functions of the Hodge numbers in terms of theta and eta functions. We specialize in this paper to generating functions of the chi(y)-genera of Hilbert schemes of n points on K3 surfaces. We determine asymptotic values of the coefficients of the chi(y)-genus for n -> infinity as well as their asymptotic profile.