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arXiv · 1110.4439

Enumerative meaning of mirror maps for toric Calabi-Yau manifolds

Kwokwai Chan·Siu-Cheong Lau·Hsian-Hua Tseng
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Abstract

We prove that the inverse of a mirror map for a toric Calabi-Yau manifold of the form $K_Y$, where $Y$ is a compact toric Fano manifold, can be expressed in terms of generating functions of genus 0 open Gromov-Witten invariants defined by Fukaya-Oh-Ohta-Ono \cite{FOOO10}. Such a relation between mirror maps and disk counting invariants was first conjectured by Gross and Siebert \cite[Conjecture 0.2 and Remark 5.1]{GS11} as part of their program, and was later formulated in terms of Fukaya-Oh-Ohta-Ono's invariants in the toric Calabi-Yau case in \cite[Conjecture 1.1]{CLL12}.

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Kwokwai Chan, Siu-Cheong Lau, Hsian-Hua Tseng. 2013-05-17. Enumerative meaning of mirror maps for toric Calabi-Yau manifolds. https://doi.org/10.1016/j.aim.2013.05.018

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