Universality of Descendent Integrals over Moduli Spaces of Stable Sheaves on $K3$ Surfaces

Abstract

We interprete results of Markman on monodromy operators as a universality statement for descendent integrals over moduli spaces of stable sheaves on $K3$ surfaces. This yields effective methods to reduce these descendent integrals to integrals over the punctual Hilbert scheme of the $K3$ surface. As an application we establish the higher rank Segre-Verlinde correspondence for $K3$ surfaces as conjectured by Göttsche and Kool.

References in corpus (1)

• Virtual Segre and Verlinde numbers of projective surfaces

Cited by in corpus (4)

• Virtual Segre and Verlinde numbers of projective surfaces
• Multiple cover formulas for K3 geometries, wall-crossing, and Quot schemes
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• Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points