Families of Lagrangian fibrations on hyperkähler manifolds |
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Authors: | Ljudmila Kamenova Misha Verbitsky |
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Institution: | 1. Department of Mathematics, Room 3-115, Stony Brook University, Stony Brook, NY 11794-3651, USA;2. Laboratory of Algebraic Geometry, Faculty of Mathematics, National Research University HSE, 7 Vavilova Str., Moscow, Russia |
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Abstract: | 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, simple hyperkähler manifold with b2?7 admits only finitely many deformation types of holomorphic Lagrangian fibrations. We also prove that all known hyperkähler manifolds are never Kobayashi hyperbolic. |
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Keywords: | Hyperkä hler manifold Holomorphic symplectic manifold Lagrangian fibration |
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