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

Yukinobu Toda

Geometry & Topology 28 (2024) 1341–1407
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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