The refined local Donaldson–Thomas theory of curves

Monavari, Sergej

doi:10.2140/gt.2026.30.3423

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ISSN (electronic): 1364-0380

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The refined local Donaldson–Thomas theory of curves

Sergej Monavari

Geometry & Topology 30 (2026) 3423–3484

DOI: 10.2140/gt.2026.30.3423

Abstract

We solve the K-theoretically refined Donaldson–Thomas theory of local curves in arbitrary genus and degree. Our results avoid degeneration techniques, but rather exploit direct localisation methods to reduce the refined Donaldson–Thomas partition function to the equivariant intersection theory of skew nested Hilbert schemes on smooth projective curves. In the refined limit, our results establish a formula for the refined topological string partition function of local curves conjecturally proposed by Aganagic and Schaeffer. In the second part, we show that analogous structural results hold for the refined Pandharipande–Thomas theory of local curves. As an application, we deduce the K-theoretic DT/PT correspondence for local curves in arbitrary genus, as conjectured by Nekrasov and Okounkov.

Thanks to the recent machinery developed by Pardon, we expect our explicit results on local curves to play a key role towards the proof of the refined GW/PT conjectural correspondence of Brini and Schuler for all smooth Calabi–Yau threefolds.

Keywords

Donaldson–Thomas theory, refined topological string partition function, skew nested Hilbert schemes

Mathematical Subject Classification

Primary: 14N35

Secondary: 14C05

References

Publication

Received: 26 November 2025

Revised: 20 April 2026

Accepted: 18 May 2026

Published: 12 October 2026

Proposed: Dan Abramovich

Seconded: Marc Levine, Arend Bayer

Authors

Sergej Monavari
Department of Mathematics “Tullio Levi-Civita” Università degli Studi di Padova Padova Italy

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Volume 30, issue 9 (2026)