Geodesic
Lagrangian fibrations on hyperk\"ahler fourfolds
Izvestiya. Mathematics , Tome 78 (2014) no. 1, pp. 22-33.

Voir la notice de l'article provenant de la source Math-Net.Ru

In answer to the strong form of a question posed by Beauville, we give a short geometric proof that any hyperkähler fourfold containing a Lagrangian subtorus $L$ admits a holomorphic Lagrangian fibration with fibre $L$.
Keywords: hyperkähler manifold, Lagrangian fibration. 
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D. Greb; Ch. Lehn; S. Rollenske. Lagrangian fibrations on hyperk\"ahler fourfolds. Izvestiya. Mathematics , Tome 78 (2014) no. 1, pp. 22-33. http://geodesic.mathdoc.fr/item/IM2_2014_78_1_a1/

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