The log-open correspondence for two-component Looijenga pairs

Abstract

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.

27 pages. Typos fixed. Accepted version

References in corpus (17)

• The Topological Vertex
• A Mathematical Theory of the Topological Vertex
• Tropical refined curve counting from higher genera and lambda classes
• Local Gromov-Witten Invariants are Log Invariants
• Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
• The quantum tropical vertex
• Holomorphic anomaly equation for $({\mathbb{P}}^2,E)$ and the Nekrasov-Shatashvili limit of local ${\mathbb{P}}^2$
• Stable maps to Looijenga pairs
• Virtual push-forwards
• Higher genus relative and orbifold Gromov-Witten invariants
• Refined floor diagrams from higher genera and lambda classes
• Open/closed Correspondence via Relative/local Correspondence
• The local-orbifold correspondence for simple normal crossings pairs
• Open/Closed BPS Correspondence and Integrality
• Gromov-Witten theory of bicyclic pairs
• Remarks on gluing punctured logarithmic maps
• The local/logarithmic correspondence and the degeneration formula for quasimaps