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arXiv · 2201.03833

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

Georg Oberdieck
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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 G\"ottsche and Kool.

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Georg Oberdieck. 2022-01-11. Universality of Descendent Integrals over Moduli Spaces of Stable Sheaves on $K3$ Surfaces. https://doi.org/10.3842/sigma.2022.076

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