The log-open correspondence for maximal-boundary log Calabi–Yau surfaces

Let $Y(D)$ be a log Calabi–Yau surface with maximal boundary, let $d$ be a $D$-convex curve class, and let $Y^{\rm op}(D)=(Y^{(l)}\setminus D^{(l)},L)$ be the associated open geometry, with relative class identification $\iota:\operatorname{H}^{\rm rel}_2(Y^{\rm op}(D),\mathbb{Z})\to\operatorname{H}_2(Y,\mathbb{Z})$. The log-open correspondence.

$$O_{0;\iota^{-1}(d)}(Y^{\rm op}(D))=\left(\prod_{k=1}^l\frac{(-1)^{d\cdot D_k-1}}{d\cdot D_k}\right)N^{\log}_{0,d}(Y(D)).$$

This proposes an equality between genus-zero open Gromov–Witten counts of a Calabi–Yau threefold with Lagrangian boundary conditions and stationary maximal-tangency log invariants of the surface; no resolution is supplied.