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## Families of Lagrangian fibrations on hyperkahler manifolds

Advances in Mathematics. 2014. Vol. 260. P. 401-413.
Kamenova L., Verbitsky M.

A holomorphic Lagrangian fibration on a holomorphically symplectic manifold is a holomorphic map with Lagrangian fibers. It is known that a given compact manifold admits only finitely many holomorphic symplectic structures, up to deformation. We prove that a given compact manifold with \$b_2 \geq 7\$ admits only finitely many deformation types of holomorphic Lagrangian fibrations. We also prove that all known hyperkahler manifolds are never Kobayashi hyperbolic.