Higher direct images of Lagrangian fibrations

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.

26 pages

Cited by in corpus (6)

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• Ergodic complex structures on hyperkahler manifolds: an erratum