Isotrivial Lagrangian fibrations of hyper-Kähler manifolds of K3^[n] and Kum_n type

Abstract: 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.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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