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Higher direct images of Lagrangian fibrations

Daisuke Matsushita
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Abstract

We prove that the higher direct images of the dualizing sheaf of a Lagrangian fibration between smooth projective manifolds are isomorphic to the cotangent bundles of base space. As a corollary, we obtain that every Hodge number of the base space of a fibre space of an irreducible symplectic manifold is the same to that of a projective space if the base space is smooth.

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Daisuke Matsushita. 2000-10-29. Higher direct images of Lagrangian fibrations. https://arxiv.org/abs/math/0010283

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