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Lagrangian fibrations on generalized Kummer varieties

Martin G. Gulbrandsen
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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 K^n(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 K^n(A) carries a divisor with vanishing Beauville-Bogomolov square.

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Martin G. Gulbrandsen. 2005-10-07. Lagrangian fibrations on generalized Kummer varieties. https://arxiv.org/abs/math/0510145

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