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arXiv · 2211.12182

The categorical DT/PT correspondence and quasi-BPS categories for local surfaces

Tudor Pădurariu·Yukinobu Toda
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Abstract

We construct semiorthogonal decompositions of Donaldson-Thomas (DT) categories for reduced curve classes on local surfaces into products of quasi-BPS categories and Pandharipande-Thomas (PT) categories, giving a categorical analogue of the numerical DT/PT correspondence for Calabi-Yau 3-folds. The main ingredient is a categorical wall-crossing formula for DT/PT quivers (which appear as Ext-quivers in the DT/PT wall-crossing) proved in our previous paper. We also study quasi-BPS categories of points on local surfaces and propose conjectural computations of their K-theory analogous to formulas already known for the three dimensional affine space.

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Tudor Pădurariu, Yukinobu Toda. 2022-11-22. The categorical DT/PT correspondence and quasi-BPS categories for local surfaces. https://doi.org/10.1112/mod.2025.10017

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