This article is cited in 5 papers

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

Georg Oberdieck

Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany

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.

Keywords: moduli spaces of sheaves, $K3$ surfaces, descendent integrals.

MSC: 14D20, 14J28, 14J80, 14J60

Received: January 23, 2022; in final form October 6, 2022; Published online October 13, 2022

Language: English

DOI: 10.3842/SIGMA.2022.076

Bibliographic databases:

• 

ArXiv: 2201.03833