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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.12182 |
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| _version_ | 1866912820496433152 |
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| author | Pădurariu, Tudor Toda, Yukinobu |
| author_facet | Pădurariu, Tudor Toda, Yukinobu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_12182 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The categorical DT/PT correspondence and quasi-BPS categories for local surfaces Pădurariu, Tudor Toda, Yukinobu Algebraic Geometry 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. |
| title | The categorical DT/PT correspondence and quasi-BPS categories for local surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2211.12182 |