Donaldson–Scaduto conjecture on collapsing special Lagrangians
Donaldson–Scaduto conjecture on collapsing special Lagrangians
Let be a -parameter family of compact Calabi–Yau manifolds with metrics admitting special Lagrangian fibration structures and with bounded diameters, and let be a holomorphic curve in . Assume that are collapsing, meaning
where is an integral affine manifold equipped with a Hessian-type metric outside a codimension-two locus. Donaldson–Scaduto conjecture. The curves converge to a tropical curve on . This folklore conjecture motivates the use of tropical geometry in collapsing Calabi–Yau manifolds. The paper says it has been proved only in specific settings, including algebraic curves in with incidence relations and torus fiber bundles, and remains unresolved for compact -Calabi–Yau manifolds.
Sources & referencesView supporting material
Primary source
Shih-Kai Chiu and Yu-Shen Lin, “Special Lagrangian submanifolds in K3-fibered Calabi-Yau 3-folds”, arXiv:2410.17662 (2024).
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