Rank zero Segre integrals on Hilbert schemes of points on surfaces

TL;DR

This paper proves a conjecture relating to rank zero Segre integrals on Hilbert schemes of points on surfaces, thereby determining these integrals for all surfaces.

Contribution

It establishes the Marian-Oprea-Pandharipande conjecture for rank zero Segre series on Hilbert schemes of points on surfaces.

Findings

Conjecture on rank zero Segre series proven.

Segre integrals on Hilbert schemes determined for all surfaces.

Advances understanding of geometric invariants on Hilbert schemes.

Abstract

We prove the conjecture of Marian-Oprea-Pandharipande on the Segre series associated to a rank zero class. Hence the rank zero Segre integrals on the Hilbert schemes of points for all surfaces are determined.