English

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

Algebraic Geometry 2026-01-14 v1

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.

Keywords

Cite

@article{arxiv.2211.12182,
  title  = {The categorical DT/PT correspondence and quasi-BPS categories for local surfaces},
  author = {Tudor Pădurariu and Yukinobu Toda},
  journal= {arXiv preprint arXiv:2211.12182},
  year   = {2026}
}

Comments

42 pages