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 $n\geq{3}$.