Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrangian fibrations on generalized Kummer varieties   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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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin