Lagrangian fibrations on generalized Kummer varieties

2007Bulletin de la Société mathématique de FrancePhysics and Astronomy被引 6开放获取

摘要

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.

引用本文（GB/T 7714）

Martin G. Gulbrandsen. Lagrangian fibrations on generalized Kummer varieties[J]. Bulletin de la Société mathématique de France, 2007.

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DOI：https://doi.org/10.24033/bsmf.2535

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