Finiteness of Lagrangian fibrations with fixed invariants

摘要

We prove finiteness of the deformation classes of hyperkahler Lagrangian fibrations in any fixed dimension with fixed Fujiki constant and discriminant of the Beauville-Bogomolov-Fujiki lattice. We also prove there are only finitely many deformation classes of hyperkahler Lagrangian fibrations with an ample line bundle of a given degree on the general fibre of the fibration. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.