Holomorphic anomaly equations for the formal quintic
Algebraic Geometry
2020-04-21 v2
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.
Cite
@article{arxiv.1803.01409,
title = {Holomorphic anomaly equations for the formal quintic},
author = {Hyenho Lho and Rahul Pandharipande},
journal= {arXiv preprint arXiv:1803.01409},
year = {2020}
}
Comments
The structure of the paper is parallel to our earlier study of local CP2 in arXiv:1702.06096, final version