Webs of Lagrangian Tori in Projective Symplectic Manifolds

Abstract

For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperkähler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.

18 pages, minor latex problem fixed

References in corpus (1)

• Base manifolds for fibrations of projective irreducible symplectic manifolds

Cited by in corpus (6)

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• On families of lagrangian tori on hyperkaehler manifolds
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• Lagrangian fibrations on hyperkähler fourfolds