On the Donaldson-Scaduto conjecture

Abstract: This talk is based on a joint work with Yang Li. Motivated by collapsing Calabi-Yau 3-folds and G2-manifolds with Lefschetz K3 fibrations in the adiabatic setting, Donaldson and Scaduto conjectured the existence of a special Lagrangian pair-of-pants in the Calabi-Yau 3-fold $X \times \mathbb R^2$, where $X$ is either a hyperkähler K3 surface (global version) or an A2-type ALE hyperkähler 4-manifold (local version). After a brief introduction to the subject, we discuss the significance of this conjecture in the study of Calabi-Yau 3-folds and G2-manifolds, and then prove the local version of the conjecture, which in turn implies the global version for an open subset of the moduli of K3 surfaces.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

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