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

Abstract

We prove wall-crossing formula for categorical Donaldson-Thomas invariants on the resolved conifold, which categorifies 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 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.

52 pages

References in corpus (2)

• Non-commutative Donaldson-Thomas theory and the conifold
• Counting perverse coherent systems on Calabi-Yau 4-folds

Cited by in corpus (2)

• Flops and Hilbert schemes of space curve singularities
• The categorical DT/PT correspondence and quasi-BPS categories for local surfaces