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 |
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Association Epiga
2023-05-01
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| Series: | Épijournal de Géométrie Algébrique |
| Subjects: | |
| Online Access: | https://epiga.episciences.org/9818/pdf |
| _version_ | 1797248761119899648 |
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| author | Soheyla Feyzbakhsh Richard P. Thomas |
| author_facet | Soheyla Feyzbakhsh Richard P. Thomas |
| author_sort | Soheyla Feyzbakhsh |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T20:19:43Z |
| format | Article |
| id | doaj.art-99e68e1129974195bbc09f24c2fa848f |
| institution | Directory Open Access Journal |
| issn | 2491-6765 |
| language | English |
| last_indexed | 2024-04-24T20:19:43Z |
| publishDate | 2023-05-01 |
| publisher | Association Epiga |
| record_format | Article |
| series | Épijournal de Géométrie Algébrique |
| spelling | doaj.art-99e68e1129974195bbc09f24c2fa848f2024-03-22T09:12:47ZengAssociation EpigaÉpijournal de Géométrie Algébrique2491-67652023-05-01Volume 710.46298/epiga.2023.volume7.98189818Curve counting and S-dualitySoheyla FeyzbakhshRichard P. Thomashttps://orcid.org/0000-0002-7585-9691We 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.https://epiga.episciences.org/9818/pdfmathematics - algebraic geometryhigh energy physics - theory14n35, 14d20, 14j60, 14f05 |
| spellingShingle | Soheyla Feyzbakhsh Richard P. Thomas Curve counting and S-duality Épijournal de Géométrie Algébrique mathematics - algebraic geometry high energy physics - theory 14n35, 14d20, 14j60, 14f05 |
| title | Curve counting and S-duality |
| title_full | Curve counting and S-duality |
| title_fullStr | Curve counting and S-duality |
| title_full_unstemmed | Curve counting and S-duality |
| title_short | Curve counting and S-duality |
| title_sort | curve counting and s duality |
| topic | mathematics - algebraic geometry high energy physics - theory 14n35, 14d20, 14j60, 14f05 |
| url | https://epiga.episciences.org/9818/pdf |
| work_keys_str_mv | AT soheylafeyzbakhsh curvecountingandsduality AT richardpthomas curvecountingandsduality |