The cyclic open--closed map and variations of Hodge structures

Fuente: arXiv
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Auteurs principaux: Ganatra, Sheel, Sheridan, Nick
Format: Preprint
Publié: 2025
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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