Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs

Abstract

Consider a log Calabi-Yau pair ( X , D ) (X,D) consisting of a smooth del Pezzo surface X X of degree ≥ 3 \geq 3 and a smooth anticanonical divisor D D . We prove a correspondence between genus zero logarithmic Gromov-Witten invariants of X X intersecting D D in a single point with maximal tangency and the consistent wall structure appearing in the dual intersection complex of ( X , D ) (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.