On the Chow ring of some Lagrangian fibrations

Abstract

Let $X$ be a hyperkähler variety admitting a Lagrangian fibration. Beauville's "splitting property" conjecture predicts that fibres of the Lagrangian fibration should have a particular behaviour in the Chow ring of $X$. We study this conjectural behaviour for two very classical examples of Lagrangian fibrations.

17 pages, to appear in Bulletin Belgian Math. Soc. Simon Stevin, comments welcome