Oberdieck–Pixton conjecture on Gromov–Witten potentials of elliptic fibrations

Let $X$, $B$, and an elliptic fibration

$$\pi:X\rightarrow B$$

be as in the setup, with a section $\iota:B\rightarrow X$ and normal bundle $N_\iota$. For $\gamma\in H_2(B,\mathbb Z)$, let $\mathcal{F}^{\mathsf{GW}}_{g,\gamma}$ be the associated Gromov–Witten series, let $\mathsf{QMod}=\mathbb Q[E_2,E_4,E_6]$ be the ring of quasimodular forms, and define

$$\Delta(Q)=Q\prod_{n=1}^{\infty}(1-Q^n)^{24},\qquad m=-\frac{1}{2}c_1(N_\iota)\cdot\gamma.$$

Oberdieck–Pixton conjecture. For $\gamma\in H_2(B,\mathbb Z)$,

$$\mathcal{F}^{\mathsf{GW}}_{g,\gamma}\in\frac{1}{\Delta(Q)^m}\mathsf{QMod}.$$

This extends the quasimodularity phenomenon for Gromov–Witten invariants of elliptic curves to elliptic fibrations; its resolution status is not specified in the source.