Finite generation and holomorphic anomaly equation for equivariant Gromov-Witten invariants of $K_{\mathbb{P}^1\times\mathbb{P}^1}$

Abstract

In this paper, we prove finite generation property and holomorphic anomaly equation for the equivariant Gromov-Witten theory of $K_{\mathbb{P}^1\times\mathbb{P}^1}$.