Higher Genus Gromov-Witten Theory of C^n/Z_n I: Holomorphic Anomaly Equations

Abstract

We study the structure of higher genus Gromov-Witten theory of the quotient stack $[{\mathbb{C}}^n/{\mathbb{Z}}_n]$. We prove holomorphic anomaly equations for $[{\mathbb{C}}^n/{\mathbb{Z}}_n]$, generalizing previous results of Lho-Pandharipande arXiv:1804.03168 for the case of $[{\mathbb{C}}^3/{\mathbb{Z}}_3]$ and ours arXiv:2211.15878 for the case $[{\mathbb{C}}^5/{\mathbb{Z}}_5]$ to arbitrary $n\ge 3$.

Expositional changes, more details, 56 pages, to appear in Advances in Mathematics