Curve counting and S-duality
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866918446157004800 |
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| author | Feyzbakhsh, Soheyla Thomas, Richard P. |
| author_facet | Feyzbakhsh, Soheyla Thomas, Richard P. |
| contents | We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as $\mathbb P^3$ or the quintic threefold.
We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth bundles over Hilbert schemes of ideal sheaves of curves and points in $X$.
When $X$ is Calabi-Yau this gives a simple wall crossing formula expressing curve counts (and so ultimately Gromov-Witten invariants) in terms of counts of D4-D2-D0 branes. These latter invariants are predicted to have modular properties which we discuss from the point of view of S-duality and Noether-Lefschetz theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_03037 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Curve counting and S-duality Feyzbakhsh, Soheyla Thomas, Richard P. Algebraic Geometry High Energy Physics - Theory 14N35, 14D20, 14J60, 14F05 We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as $\mathbb P^3$ or the quintic threefold. We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth bundles over Hilbert schemes of ideal sheaves of curves and points in $X$. When $X$ is Calabi-Yau this gives a simple wall crossing formula expressing curve counts (and so ultimately Gromov-Witten invariants) in terms of counts of D4-D2-D0 branes. These latter invariants are predicted to have modular properties which we discuss from the point of view of S-duality and Noether-Lefschetz theory. |
| title | Curve counting and S-duality |
| topic | Algebraic Geometry High Energy Physics - Theory 14N35, 14D20, 14J60, 14F05 |
| url | https://arxiv.org/abs/2007.03037 |