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arXiv · 1201.2369

Webs of Lagrangian Tori in Projective Symplectic Manifolds

Jun-Muk Hwang·Richard M. Weiss
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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.

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Jun-Muk Hwang, Richard M. Weiss. 2012-01-13. Webs of Lagrangian Tori in Projective Symplectic Manifolds. https://doi.org/10.1007/s00222-012-0407-2

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