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A short proof of a conjecture of Matsushita

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arxiv 2209.00604 v2 pith:NNDXF22S submitted 2022-09-01 math.AG

Benjamin Bakker This is my paper · ORCID
classification math.AG
keywords conjecturelagrangianmatsushitavoisinahlerargumentsbuildcomplete
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In this note we build on the arguments of van Geemen and Voisin to prove a conjecture of Matsushita that a Lagrangian fibration of an irreducible hyperk\"ahler manifold is either isotrivial or of maximal variation. We also complete a partial result of Voisin regarding the density of torsion points of sections of Lagrangian fibrations.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Parabolic automorphisms of hyperk{\"a}hler manifolds: Orbits and Betti maps

    math.AG 2025-02 conditional novelty 6.0 of 10

    For parabolic automorphisms of hyperkähler manifolds with a Lagrangian fibration, the translation vector has maximal rank, making fibers with finite-order or dense orbits dense in the base.

  2. Hodge theory and o-minimality at CIRM

    math.AG 2025-02 unverdicted

    Survey lecture notes connecting o-minimality, Ax-Schanuel theorems, and the Zilber-Pink conjecture for Hodge loci, with no new results.

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