Conférencier : Olivier Martin, IMPA

Résumé : I will present a classification result for Lagrangian fibrations of hyper-Kähler manifolds of K3^[n] and Kum_n types up to Tate-Shafarevich twist/degenerate twistor deformation. This improvement on the work of Markman is made possible by a recent breakthrough of Verbitsky-Soldatenkov which ensures that a degenerate twistor deformation of a Lagrangian fibration is Kähler. As a consequence, we prove that the only isotrivial Lagrangian fibrations of hyper-Kähler manifolds of K3^[n] and Kum_n type are the obvious ones. This is joint work with Yoonjoo Kim and Radu Laza.