Base manifolds for Lagrangian fibrations on hyperkähler manifolds

Abstract

We show that the base manifold of a Lagrangian fibration on a hyperkähler manifold is isomorphic to complex projective space. This generalises a theorem of J.-M. Hwang to the Kähler case.

4 pages; v2: minor changes, final version, to appear in IMRN

References in corpus (2)

• Base manifolds for fibrations of projective irreducible symplectic manifolds
• On families of lagrangian tori on hyperkaehler manifolds

Cited by in corpus (8)

• Induced Automorphisms on Irreducible Symplectic Manifolds
• Monodromy Invariants and Polarization Types of Generalized Kummer Fibrations
• Fujiki relations and fibrations of irreducible symplectic varieties
• On polarization types of Lagrangian fibrations
• Computing Riemann-Roch polynomials and classifying hyper-Kähler fourfolds
• Complex Symplectic Lie Algebras with Large Abelian Subalgebras
• Special Kähler geometry and holomorphic Lagrangian fibrations
• The monodromy of compact Lagrangian fibrations