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

TL;DR

This paper establishes finite generation and holomorphic anomaly equations for the equivariant Gromov-Witten invariants of the total space of the canonical bundle over  imes , advancing understanding in algebraic geometry and string theory.

Contribution

It proves the finite generation property and holomorphic anomaly equations specifically for the equivariant Gromov-Witten theory of this Calabi-Yau threefold.

Findings

Finite generation property established for the invariants.

Holomorphic anomaly equations derived for the theory.

Results contribute to mirror symmetry and enumerative geometry.

Abstract

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