Finite-generation conjecture for quasimap potentials of K3 fibrations

Let $X\rightarrow B$ be a K3 fibration and, for $\gamma\in H_2(B,\mathbb Z)$, let $\mathcal{F}^{\mathsf{SQ}}_{g,\gamma}$ be the associated quasimap series. Define

$$L(q)=(1-4^4q)^{-1/4},\qquad A_1'(q)=q\frac{\partial}{\partial q}I_1^{K3}(q),$$

and

$$X(q)=\frac{q\frac{\partial}{\partial q}A_1'(q)}{1+A_1'(q)},\qquad \mathsf{QKF}=\mathbb C[L^{\pm4},A_1',X].$$

K3-fibration finite-generation conjecture. For $\gamma\in H_2(B,\mathbb Z)$,

$$\mathcal{F}^{\mathsf{SQ}}_{g,\gamma}\in\mathsf{QKF}.$$

This is one of the proposed finite-generation properties for K3-fibration quasimap potentials, intended to yield consequences for Gromov–Witten potentials through wall crossing; the source provides no resolution status.