Universality of Descendent Integrals over Moduli Spaces of Stable Sheaves on 𝛫3 Surfaces

Abstract

We interpret the results of Markman on monodromy operators as a universality statement for descendant integrals over moduli spaces of stable sheaves on 𝛫3 surfaces. This yields effective methods to reduce these descendant integrals to integrals over the punctual Hilbert scheme of the 𝛫3 surface. As an application, we establish the higher rank Segre-Verlinde correspondence for 𝛫3 surfaces as conjectured by Göttsche and Kool.