Webs of Lagrangian tori in projective symplectic manifolds |
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Authors: | Jun-Muk Hwang Richard M Weiss |
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Institution: | 1. Korea Institute for Advanced Study, Hoegiro 87, Seoul, 130-722, Korea 2. Department of Mathematics, Tufts University, 503 Boston Avenue, Medford, MA, 02155, USA
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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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