Geodesic
The log-open correspondence for two-component Looijenga pairs
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e102

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A two-component Looijenga pair is a rational smooth projective surface with an anticanonical divisor consisting of two transversally intersecting curves. We establish an all-genus correspondence between the logarithmic Gromov–Witten theory of a two-component Looijenga pair and open Gromov–Witten theory of a toric Calabi–Yau threefold geometrically engineered from the surface geometry. This settles a conjecture of Bousseau, Brini and van Garrel in the case of two boundary components. We also explain how the correspondence implies BPS integrality for the logarithmic invariants and provides a new means for computing them via the topological vertex method. 
Schuler, Yannik. The log-open correspondence for two-component Looijenga pairs. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e102. doi: 10.1017/fms.2025.10042
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