局部P^2的Gromov-Witten不变量与模形式
代数几何
2023-02-22 v2 数学物理
math.MP
辛几何
摘要
我们构造了在具有Gamma_1(3)级结构的椭圆曲线E_y的模空间上的Fock空间层，源于H^1(E_y)的几何量子化，以及该Fock层的一个全局截面。该全局截面在适当极限点附近与局部P^2及orbifold C^3/mu_3的Gromov-Witten势重合。这证明了局部P^2的Gromov-Witten势是群Gamma_1(3)的拟模函数，正如Aganagic-Bouchard-Klemm所预测，并证明了[C^3/mu_3]在所有亏格下的Crepant Resolution猜想。
引用
@article{arxiv.1804.03292,
title = {Gromov-Witten Invariants of Local P^2 and Modular Forms},
author = {Tom Coates and Hiroshi Iritani},
journal= {arXiv preprint arXiv:1804.03292},
year = {2023}
}
备注
131 pages, 9 figures; fully commented source code included as ancillary file; for video of talk, see: https://www.youtube.com/watch?v=raqkmHxCJYI and https://www.youtube.com/watch?v=sRMESF1TSOA v2: final version, to appear in Kyoto Journal of Mathematics