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arXiv · 1503.07323

On a conjecture of Matsushita

Bert van Geemen·Claire Voisin
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Abstract

We prove a weak version of a conjecture of Matsushita saying that for a Lagrangian fibration on a hyper-Kaehler manifold $X$, the moduli map for the fibers is either generically of maximal rank or constant. Assuming the base is smooth and $b_2(X)-\rho(X)\geq5$, we prove the conjecture for a very general deformation of $X$ with constant N\'eron-Severi group.

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Bert van Geemen, Claire Voisin. 2015-03-25. On a conjecture of Matsushita. https://arxiv.org/abs/1503.07323

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