Lagrangian fibrations on generalized Kummer varieties
Abstract
We investigate the existence of Lagrangian fibrations on the generalized Kummer varieties of Beauville. For a principally polarized abelian surface A of Picard number one we find the following: The Kummer variety Kn(A) is birationally equivalent to another irreducible symplectic variety admitting a Lagrangian fibration, if and only if n is a perfect square. And this is the case if and only if Kn(A) carries a divisor with vanishing Beauville-Bogomolov square.
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