The stationary descendent Gromov–Witten formula for primitive K3 classes

Let $S$ be a K3 surface and let $\beta\in H_2(S,\mathbb Z)$ be primitive. For cohomology classes $\gamma_0,\gamma_1,\ldots\in H^*(S)$, define the partition function $Z_\beta(\gamma_0,\gamma_1,\ldots)$ by the exponential generating series of descendent invariants, and let $(\gamma_1,\gamma_2)=\int_S\gamma_1\cup\gamma_2$ be the intersection pairing. Let $A_k(q)$, $B_k(q)$, and $C_{k\ell}(q)$ be the power series appearing in the formula, and let $\Delta(q)$ be the discriminant series. Stationary descendent formula. If $\deg(\gamma_i)>0$ for all $i$, then

$$Z_\beta(\gamma_0,\gamma_1,\ldots)=\operatorname{Coeff}_{\beta^2/2}\left[\frac{1}{\Delta(q)}\exp\left(\sum_{k\geq0}(\gamma_k,\beta)A_k(q)+\sum_{k\geq0}(\gamma_k,1)B_k(q)+\frac12\sum_{k,\ell\geq0}(\gamma_k\cdot\gamma_\ell)C_{k\ell}(q)\right)\right].$$

This would determine all primitive stationary descendent invariants of a K3 surface. The formula is presented as conjectural in the paper and is the main input for the proposed effective computation of invariants.