Quasi-modularity and holomorphic anomaly equation for the twisted Gromov-Witten theory: $\mathcal{O}(3)$ over $\mathbb{P}^2$

Abstract

In this paper, we prove quasi-modularity property for the twisted Gromov-Witten theory of O(3) over P 2 . Meanwhile, we derive its holomorphic anomaly equation.Ω τ(q) g

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

“…In the past years, many works has been done about the finite generation and holomorphic anomaly equation for (non-)compact Calabi-Yau 3-fold and also twisted theory of Calabi-Yau type (c.f. [3], [5], [8], [9], [10], [11], [15]). Most of the examples studied are about the models of one Kähler parameter.…”