The Virasoro constraints conjecture for K3 surfaces with fiber and point insertions

Let $S$ be a K3 surface, let $\gamma_a$ be a homogeneous basis of $H^*(S)$ with $\gamma_a\in H^{p_a,q_a}(S)$, and set $b_a=p_a-1/2$. Let $[\alpha]^p_q$ denote the coefficient of $x^q$ in $(x+\alpha)(x+\alpha+1)\cdots(x+\alpha+p)$. Virasoro constraints conjecture. Assuming all insertions satisfy $\gamma_{a_i}\in\\{F,\mathsf p\\}$, there exist rational coefficients $w_{k,m}\in\mathbb Q$ such that the displayed Virasoro relation in the source holds for every relevant $k$ and the corresponding reduced Gromov–Witten invariants. This conjecture proposes Virasoro constraints in a special case motivated by known constraints for $T^*\mathbb P^1$ and numerical computations; the coefficients $w_{k,m}$ are not specified by the statement.