Categorical wall-crossing formula for Donaldson-Thomas theory on the resolved conifold
Algebraic Geometry
2024-05-22 v1 High Energy Physics - Theory
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.
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Cite
@article{arxiv.2109.07064,
title = {Categorical wall-crossing formula for Donaldson-Thomas theory on the resolved conifold},
author = {Yukinobu Toda},
journal= {arXiv preprint arXiv:2109.07064},
year = {2024}
}
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52 pages