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

Toda, Yukinobu¹

¹ Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Japan

Geometry & topology, Tome 28 (2024) no. 3, pp. 1341-1407.

Résumé

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.

Détail

DOI : 10.2140/gt.2024.28.1341

Keywords: Donaldson–Thomas invariants, matrix factorizations

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