Categorical wall-crossing formula for Donaldson–Thomas theory on the resolved conifold

Toda, Yukinobu

doi:10.2140/gt.2024.28.1341

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Categorical wall-crossing formula for Donaldson–Thomas theory on the resolved conifold

Yukinobu Toda

Geometry & Topology 28 (2024) 1341–1407

DOI: 10.2140/gt.2024.28.1341

Abstract

We prove a wall-crossing formula for categorical Donaldson–Thomas invariants on the resolved conifold, which categorifies the Nagao–Nakajima wall-crossing formula for numerical DT invariants on it. The categorified Hall products are used to describe the wall-crossing formula as semiorthogonal decompositions. A successive application of the categorical wall-crossing formula yields semiorthogonal decompositions of categorical Pandharipande–Thomas stable pair invariants on the resolved conifold, which categorify the product expansion formula of the generating series of numerical PT invariants on it.

Keywords

Donaldson–Thomas invariants, matrix factorizations

Mathematical Subject Classification

Primary: 14N35

Secondary: 18G80

References

Publication

Received: 20 January 2022

Revised: 14 August 2022

Accepted: 11 September 2022

Published: 10 May 2024

Proposed: Jim Bryan

Seconded: Mark Gross, Richard P Thomas

Authors

Yukinobu Toda
Kavli Institute for the Physics and Mathematics of the Universe (WPI) University of Tokyo Kashiwa Japan

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Volume 28, issue 3 (2024)