Consider a log Calabi-Yau pair (X, D) consisting of a smooth del Pezzo surface X of degree ≥ 3 and a smooth anticanonical divisor D. We prove a correspondence between genus zero logarithmic Gromov-Witten invariants of X intersecting D in a single point with maximal tangency and the consistent wall structure appearing in the dual intersection complex of (X, D) from the Gross-Siebert reconstruction algorithm. More precisely, the logarithm of the product of functions attached to unbounded walls in the consistent wall structure gives a generating function for these invariants. Contents 42 6. Torsion points 49 7. Explicit calculations 52 Appendix A. Artin fans and logarithmic modifications 63 References 66
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