# Local projectivity of Lagrangian fibrations on Hyperk\"ahler manifolds

14 Dec 2017  ·  Campana Frederic ·

We show that if $f:X\to B$ is a Lagrangian fibration from a compact connected K\"ahler hyperk\"ahler manifold $X$ onto a projective normal variety $B$, then $f$ is locally projective. This answers a question raised by L. Kamenova and strengthens a former result (\cite{Ca05}, Proposition 2.1), according to which the smooth fibres of $f$ are projective... The proof below does not use the known additional results concerning fibres and base in this specific context). read more

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Algebraic Geometry