The log-open correspondence for two-component Looijenga pairs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913920231407616 |
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| author | Schuler, Yannik |
| author_facet | Schuler, Yannik |
| contents | A two-component Looijenga pair is a rational smooth projective surface with an anticanonical divisor consisting of two transversally intersecting curves. We establish an all-genus correspondence between the logarithmic Gromov-Witten theory of a two-component Looijenga pair and open Gromov-Witten theory of a toric Calabi-Yau threefold geometrically engineered from the surface geometry. This settles a conjecture of Bousseau, Brini and van Garrel in the case of two boundary components. We also explain how the correspondence implies BPS integrality for the logarithmic invariants and provides a new means for computing them via the topological vertex method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15412 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The log-open correspondence for two-component Looijenga pairs Schuler, Yannik Algebraic Geometry 14N35 A two-component Looijenga pair is a rational smooth projective surface with an anticanonical divisor consisting of two transversally intersecting curves. We establish an all-genus correspondence between the logarithmic Gromov-Witten theory of a two-component Looijenga pair and open Gromov-Witten theory of a toric Calabi-Yau threefold geometrically engineered from the surface geometry. This settles a conjecture of Bousseau, Brini and van Garrel in the case of two boundary components. We also explain how the correspondence implies BPS integrality for the logarithmic invariants and provides a new means for computing them via the topological vertex method. |
| title | The log-open correspondence for two-component Looijenga pairs |
| topic | Algebraic Geometry 14N35 |
| url | https://arxiv.org/abs/2404.15412 |