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For a Lagrangian torus A in a simply-connected projective symplectic manifoldM, we prove that M has a hypersurface disjoint from a deformation of A. Thisimplies that a Lagrangian torus in a compact hyperk\"ahler manifold is a fiberof an almost holomorphic Lagrangian fibration, giving an affirmative answer toa question of Beauville's. Our proof employs two different tools: the theory ofaction-angle variables for algebraically completely integrable Hamiltoniansystems and Wielandt's theory of subnormal subgroups.

Webs of Lagrangian Tori in Projective Symplectic Manifolds