Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperkahler manifolds of Jacobian type   In this paper we define the notion of a hyperk\"ahler manifold (potentially)
of Jacobian type. If we view hyperk\"ahler manifolds as "abelian varieties",
then those of Jacobian type should be viewed as "Jacobian varieties". Under a
minor assumption on the polarization, we show that a very general polarized
hyperk\"ahler fourfold $F$ of $K3^{[2]}$-type is not of Jacobian type. As a
potential application, we conjecture that if a cubic fourfold is rational then
its variety of lines is of Jacobian type. Under some technical assumption, it
is proved that the variety of lines on a rational cubic fourfold is potentially
of Jacobian type. We also prove the Hodge conjecture in degree 4 for a generic
$F$ of $K3^{[2]}$-type.

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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex