The stationary log/local correspondence for maximal log Calabi–Yau pairs

Let $(Y,D=D_1+\dots+D_l)$ be a log-smooth log Calabi–Yau pair of maximal boundary. For $\mathsf{m}=1,\dots,l+1$, let $Y^{(\mathsf{m})}=\operatorname{Tot}(\bigoplus_{k\geq\mathsf{m}}\mathcal{O}_Y(-D_k))$, and let $D^{(\mathsf{m})}$ be the preimage of $\bigcup_{k<\mathsf{m}}D_k$. Let $d$ be a $D$-convex curve class, and let $N^{\rm \log}_{0,d}(Y^{(\mathsf{m})}(D^{(\mathsf{m})}))$ denote the genus-zero maximal-tangency stationary log Gromov–Witten invariant. The stationary log/local correspondence. For $1\leq\mathsf{n}<\mathsf{m}\leq l+1$,

$$N^{\rm \log}_{0,d}(Y^{(\mathsf{m})}(D^{(\mathsf{m})}))=\left(\prod_{i=\mathsf{n}}^{\mathsf{m}-1}(-1)^{d\cdot D_i+1}d\cdot D_i\right)N^{\rm \log}_{0,d}(Y^{(\mathsf{n})}(D^{(\mathsf{n})})).$$

In particular, $N^{\rm \log}_{0,d}(Y(D))=\left(\prod_{i=1}^l(-1)^{d\cdot D_i+1}d\cdot D_i\right)N^{\rm loc}_{0,d}(Y(D))$. This extends the genus-zero stationary log/local correspondence from smooth divisors to maximal-boundary simple normal-crossing pairs; its status is not resolved in the supplied text.