We give close formulas for the counting functions of rational curves on complete intesection Calabi-Yau manifolds in terms of special solutions of generalized hypergeometric differential systems. For the one modulus cases we derive a differential equation for the Mirror map, which can be viewed as a generalization of the Schwarzian equation. We also derive a nonlinear seventh order differential equation which directly governs the Prepotential.
@inproceedings{a1996a,
title={A note on ODEs from mirror symmetry},
author={A Klemm, BH Lian, SS Roan, and Shing-Tung Yau},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204049200362126},
pages={301-323},
year={1996},
}
A Klemm, BH Lian, SS Roan, and Shing-Tung Yau. A note on ODEs from mirror symmetry. 1996. pp.301-323. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204049200362126.