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1 results

  • The log-open correspondence for two-component Looijenga pairs

  • Part of
  • Yannik Schuler
  • Journal:
    Forum of Mathematics, Sigma / Volume 13 / 2025
    Published online by Cambridge University Press:
    26 June 2025, e102
    • Article
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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.