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arXiv · 1712.01902

Local projectivity of Lagrangian fibrations on Hyperk\"ahler manifolds

Frederic Campana
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Abstract

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).

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Frederic Campana. 2017-12-05. Local projectivity of Lagrangian fibrations on Hyperk\"ahler manifolds. https://arxiv.org/abs/1712.01902

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