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arXiv · 2211.12178

The local categorical DT/PT correspondence

Tudor Pădurariu·Yukinobu Toda
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Abstract

In this paper, we prove the categorical wall-crossing formula for certain quivers containing the three loop quiver, which we call DT/PT quivers. These quivers appear as Ext-quivers for the wall-crossing of DT/PT moduli spaces on Calabi-Yau 3-folds. The resulting formula is a semiorthogonal decomposition which involves quasi-BPS categories studied in our previous papers, and we regard it as a categorical analogue of the numerical DT/PT correspondence. As an application, we prove a categorical DT/PT correspondence for sheaves supported on reduced plane curves in the affine three dimensional space.

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Tudor Pădurariu, Yukinobu Toda. 2022-11-22. The local categorical DT/PT correspondence. https://arxiv.org/abs/2211.12178

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