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arXiv · 1803.01409

Holomorphic anomaly equations for the formal quintic

Hyenho Lho·Rahul Pandharipande
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Abstract

We define a formal Gromov-Witten theory of the quintic 3-fold via localization on CP4. Our main result is a direct geometric proof of holomorphic anomaly equations for the formal quintic in precisely the same form as predicted by B-model physics for the true Gromov-Witten theory of the quintic 3-fold. The results suggest that the formal quintic and the true quintic theories should be related by transformations which respect the holomorphic anomaly equations. Such a relationship has been recently found by Q. Chen, S. Guo, F. Janda, and Y. Ruan via the geometry of new moduli spaces.

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Hyenho Lho, Rahul Pandharipande. 2018-03-04. Holomorphic anomaly equations for the formal quintic. https://arxiv.org/abs/1803.01409

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