Multi-Component Open/Relative/Local Correspondence
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915681204699136 |
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| author | Yu, Song Zhang, Ke Zong, Zhengyu |
| author_facet | Yu, Song Zhang, Ke Zong, Zhengyu |
| contents | For a toric Calabi-Yau 3-orbifold relative to s Aganagic-Vafa outer branes, we prove a correspondence among the genus-zero open Gromov-Witten invariants with maximal winding at each brane and: (i) closed invariants of a toric Calabi-Yau (3+s)-orbifold; (ii) formal relative invariants of a formal toric Calabi-Yau (FTCY) 3-orbifold with maximal tangency to s divisors; (iii) formal relative invariants of a sequence of FTCY intermediate geometries interpolating dimensions 3 and 3+s. The correspondence provides examples of the log/local principle of van Garrel-Graber-Ruddat in the multi-component setting and the refined conjecture of Brini-Bousseau-van Garrel via intermediate geometries. It also establishes the multi-component case of the open/closed correspondence proposed by Lerche-Mayr and studied by Liu-Yu. As an application, we obtain examples of the conjecture of Klemm-Pandharipande on the integrality of BPS invariants of higher-dimensional toric Calabi-Yau manifolds. Along the way, we set the basic stages of the relative Gromov-Witten theory of higher-dimensional FTCY orbifolds, generalizing the case of smooth 3-folds by Li-Liu-Liu-Zhou. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15074 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-Component Open/Relative/Local Correspondence Yu, Song Zhang, Ke Zong, Zhengyu Algebraic Geometry 14N35 For a toric Calabi-Yau 3-orbifold relative to s Aganagic-Vafa outer branes, we prove a correspondence among the genus-zero open Gromov-Witten invariants with maximal winding at each brane and: (i) closed invariants of a toric Calabi-Yau (3+s)-orbifold; (ii) formal relative invariants of a formal toric Calabi-Yau (FTCY) 3-orbifold with maximal tangency to s divisors; (iii) formal relative invariants of a sequence of FTCY intermediate geometries interpolating dimensions 3 and 3+s. The correspondence provides examples of the log/local principle of van Garrel-Graber-Ruddat in the multi-component setting and the refined conjecture of Brini-Bousseau-van Garrel via intermediate geometries. It also establishes the multi-component case of the open/closed correspondence proposed by Lerche-Mayr and studied by Liu-Yu. As an application, we obtain examples of the conjecture of Klemm-Pandharipande on the integrality of BPS invariants of higher-dimensional toric Calabi-Yau manifolds. Along the way, we set the basic stages of the relative Gromov-Witten theory of higher-dimensional FTCY orbifolds, generalizing the case of smooth 3-folds by Li-Liu-Liu-Zhou. |
| title | Multi-Component Open/Relative/Local Correspondence |
| topic | Algebraic Geometry 14N35 |
| url | https://arxiv.org/abs/2512.15074 |