Curve counting and S-duality
We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-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 a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Association Epiga
2023-05-01
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| Series: | Épijournal de Géométrie Algébrique |
| Subjects: | |
| Online Access: | https://epiga.episciences.org/9818/pdf |
| Summary: | We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker
conjecture of Bayer-Macr\`i-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. |
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| ISSN: | 2491-6765 |