AGT relations for sheaves on surfaces

Neguţ, Andrei

doi:10.2140/gt.2023.27.3061

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AGT relations for sheaves on surfaces

Andrei Neguţ

Geometry & Topology 27 (2023) 3061–3094

DOI: 10.2140/gt.2023.27.3061

Abstract

We consider a natural generalization of the Carlsson–Okounkov Ext operator on the $K$ –theory groups of the moduli spaces of stable sheaves on a smooth projective surface. We compute the commutation relations between the Ext operator and the action of the deformed $W$ –algebra on $K$ –theory, which was developed by the author in previous work. The conclusion is that the Ext operator is closely related to a vertex operator, thus giving a mathematical incarnation of the Alday–Gaiotto–Tachikawa correspondence for a general algebraic surface.

Keywords

moduli spaces of sheaves on surfaces, Ext operator, AGT correspondence

Mathematical Subject Classification

Primary: 14J60

Secondary: 14D21

References

Publication

Received: 26 May 2020

Revised: 9 March 2022

Accepted: 19 March 2022

Published: 9 November 2023

Proposed: Richard P Thomas

Seconded: Lothar Göttsche, Mark Gross

Authors

Andrei Neguţ
Department of Mathematics MIT Cambridge, MA United States	Simion Stoilow Institute of Mathematics Bucharest Romania

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Volume 27, issue 8 (2023)