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arXiv · 1006.3827

A formula equating open and closed Gromov-Witten invariants and its applications to mirror symmetry

Kwokwai Chan
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Abstract

We prove that open Gromov-Witten invariants for semi-Fano toric manifolds of the form $X=\mathbb{P}(K_Y\oplus\mathcal{O}_Y)$, where $Y$ is a toric Fano manifold, are equal to certain 1-pointed closed Gromov-Witten invariants of $X$. As applications, we compute the mirror superpotentials for these manifolds. In particular, this gives a simple proof for the formula of the mirror superpotential for the Hirzebruch surface $\mathbb{F}_2$.

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Kwokwai Chan. 2010-06-19. A formula equating open and closed Gromov-Witten invariants and its applications to mirror symmetry. https://doi.org/10.2140/pjm.2011.254.275

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