The cyclic open--closed map and variations of Hodge structures
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915602653773824 |
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| author | Ganatra, Sheel Sheridan, Nick |
| author_facet | Ganatra, Sheel Sheridan, Nick |
| contents | We construct the cyclic open--closed map for the big (i.e., bulk-deformed) relative Fukaya category, in the semipositive case, and show that it is a morphism of `polarized variations of semi-infinite Hodge structures'. We also give a natural criterion for the map to be an isomorphism, which is verified for example in the context of Batyrev mirror pairs. We conclude in such Calabi-Yau cases that the rational Gromov--Witten invariants can be extracted from the relative Fukaya category, and hence that enumerative mirror symmetry is a consequence of homological mirror symmetry for Calabi--Yau mirror pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The cyclic open--closed map and variations of Hodge structures Ganatra, Sheel Sheridan, Nick Algebraic Geometry Symplectic Geometry We construct the cyclic open--closed map for the big (i.e., bulk-deformed) relative Fukaya category, in the semipositive case, and show that it is a morphism of `polarized variations of semi-infinite Hodge structures'. We also give a natural criterion for the map to be an isomorphism, which is verified for example in the context of Batyrev mirror pairs. We conclude in such Calabi-Yau cases that the rational Gromov--Witten invariants can be extracted from the relative Fukaya category, and hence that enumerative mirror symmetry is a consequence of homological mirror symmetry for Calabi--Yau mirror pairs. |
| title | The cyclic open--closed map and variations of Hodge structures |
| topic | Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2511.04498 |