Gromov-Witten invariants of local P2 andmodular forms

被引：3

作者：

Coates, Tom ^{[1
]}

Iritani, Hiroshi ^{[2
]}

机构：

[1] Imperial Coll London, Dept Math, London, England

[2] Kyoto Univ, Grad Sch Sci, Dept Math, Kyoto, Japan

来源：

KYOTO JOURNAL OF MATHEMATICS | 2021年 / 61卷 / 03期

基金：

英国工程与自然科学研究理事会; 欧洲研究理事会; 日本学术振兴会; 美国国家科学基金会;

关键词：

QUANTUM COHOMOLOGY; CREPANT RESOLUTIONS; MIRROR SYMMETRY; HODGE STRUCTURE; CYCLES; MODEL;

D O I：

10.1215/21562261-2021-0010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a sheaf of Fock spaces over the moduli space of elliptic curves E-y with Gamma(1)(3)-level structure, arising from geometric quantization of H-1(E-y), and a global section of this Fock sheaf. The global section coincides, near appropriate limit points, with the Gromov-Witten potentials of local P-2 and of the orbifold [C-3/mu(3)]. This proves that the Gromov-Witten potentials of local P-2 are quasimodular functions for the group Gamma(1)(3), as predicted by Aganagic, Bouchard, and Klemm, and it proves the crepant resolution conjecture for [C-3/mu(3)] in all genera.

引用

页码：543 / 706

页数：164

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