Special Lagrangians in Calabi-Yau $3$-folds with a K3-fibration

Abstract: Special Lagrangians form an important class of minimal submanifolds in Calabi-Yau manifolds. In this talk, we will consider the Calabi-Yau $3$-folds with a K3-fibration and the size of the K3-fibres are small. Motivated by tropical geometry, Donaldson-Scaduto conjectured that special Lagrangian collapse to ``gradient cycles" when the K3-fibres collapse. This phenomenon is similar to holomorphic curves in Calabi-Yau manifolds with collapsing special Lagrangian fibrations converging to tropical curves. Similar to the realization problem in tropical geometry, one might expect to reconstruct special Lagrangians from gradient cycles. In this talk, I will report the first theorem of this kind based on a joint work with Shih-Kai Chiu.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

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