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arXiv · 2509.24727

Mirror symmetry and open/closed correspondence for the projective line

Jinghao Yu·Zhengyu Zong
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Abstract

We study the open/closed correspondence for the projective line via mirror symmetry. More explicitly, we establish a correspondence between the generating function of disk Gromov-Witten invariants of the complex projective line $\mathbb{P}^1$ with boundary condition specified by an $S^1$-invariant Lagrangian sub-manifold $L$ and the asymptotic expansion of the $I$-function of a toric surface $\mathcal{S}$.

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Jinghao Yu, Zhengyu Zong. 2025-09-29. Mirror symmetry and open/closed correspondence for the projective line. https://arxiv.org/abs/2509.24727

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