Virtual counts on Quot schemes and the higher rank local DT/PT correspondence
| Autor: | Beentjes, Sjoerd Viktor, Ricolfi, Andrea T. |
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| Rok vydání: | 2018 |
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| Zdroj: | Math. Res. Lett., Vol. 28, no. 4 (2021), 967-1032 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4310/MRL.2021.v28.n4.a2 |
| Popis: | We show that the Quot scheme $\text{Quot}_{\mathbf{A}^3}(\mathcal{O}^r,n)$ admits a symmetric obstruction theory, and we compute its virtual Euler characteristic. We extend the calculation to locally free sheaves on smooth $3$-folds, thus refining a special case of a recent Euler characteristic calculation of Gholampour-Kool. We then extend Toda's higher rank DT/PT correspondence on Calabi-Yau $3$-folds to a local version centered at a fixed slope stable sheaf. This generalises (and refines) the local DT/PT correspondence around the cycle of a Cohen-Macaulay curve. Our approach clarifies the relation between Gholampour-Kool's functional equation for Quot schemes, and Toda's higher rank DT/PT correspondence. Comment: v2. Minor changes and corrections following referee's comments, 40 pages. Accepted for publication in Math. Res. Lett |
| Databáze: | arXiv |
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