Universality of $\mathsf{CohFT}$ of $\mathsf{Hilb}_n(S)$

Abstract

By virtue of their relation to Fulton--MacPherson compactifications, the cohomological field theory of Hilbert schemes of points on a surface, in extremal curve classes, is universally and effectively determined by the characteristic numbers of the surface and by the corresponding theory of Hilbert schemes of the affine plane. As a consequence, we compute the extremal genus 1 Gromov--Witten invariants of Hilbert schemes of all surfaces.