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Structure of higher-genus open-closed Gromov--Witten theory of π’ͺβ„™1(pβˆ’1)βŠ•π’ͺβ„™1(βˆ’pβˆ’1)

  • Shuai Guo
  • Jingyi Xu
  • Qingsheng Zhang
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Abstract

We study the closed and open Gromov--Witten potentials of the toric Calabi--Yau threefold Xp=Tot(π’ͺβ„™1(pβˆ’1)βŠ•π’ͺβ„™1(βˆ’pβˆ’1)), pβ‰₯ 2. We prove closed and open mirror symmetry under a nonvanishing condition on the torus weights, relating these potentials to topological recursion on the mirror curves. We establish polynomial structures for both the higher-genus closed potentials and the stable open potentials. We also establish double-scaling limits for topological recursion on the mirror curves. In particular, our results for the closed potentials prove the higher-genus ansatz and the double-scaling conjecture of Caporaso--Griguolo--MariΓ±o--Pasquetti--Seminara.

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Cite

BibTeXRIS
BibTeX
@misc{guo2026structure,
  title = {{Structure of higher-genus open-closed Gromov--Witten theory of $\mathcalO_\mathbbP^1(p-1)\oplus\mathcalO_\mathbbP^1(-p-1)$}},
  author = {Shuai Guo and Jingyi Xu and Qingsheng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.40257},
  eprint = {2609.40257},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.40257},
}
RIS
TY  - UNPB
TI  - Structure of higher-genus open-closed Gromov--Witten theory of π’ͺ_β„™^1(pβˆ’1)βŠ•π’ͺ_β„™^1(βˆ’pβˆ’1)
AU  - Shuai Guo
AU  - Jingyi Xu
AU  - Qingsheng Zhang
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.40257
UR  - https://arxiv.org/abs/2609.40257
AB  - We study the closed and open Gromov--Witten potentials of the toric Calabi--Yau threefold X_p=Tot(π’ͺ_β„™^1(pβˆ’1)βŠ•π’ͺ_β„™^1(βˆ’pβˆ’1)), pβ‰₯ 2. We prove closed and open mirror symmetry under a nonvanishing condition on the torus weights, relating these potentials to topological recursion on the mirror curves. We establish polynomial structures for both the higher-genus closed potentials and the stable open potentials. We also establish double-scaling limits for topological recursion on the mirror curves. In particular, our results for the closed potentials prove the higher-genus ansatz and the double-scaling conjecture of Caporaso--Griguolo--MariΓ±o--Pasquetti--Seminara.
ER  -