. SG ] 2 3 Ja n 20 04 Symplectic invariants of some families of Lagrangian T 3 - fibrations Ricardo Castaño Bernard
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Families of Lagrangian fibrations on hyperkähler manifolds
A holomorphic Lagrangian fibration on a holomorphically symplectic manifold is a holomorphic map with Lagrangian fibers. It is known (due to Huybrechts) that a given compact manifold admits only finitely many holomorphic symplectic structures, up to deformation. We prove that a given compact manifold with b2 > 7 admits only finitely many deformation types of holomorphic Lagrangian fibrations.
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