Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A period differential equation for a family of $K3$ surfaces and the
  Hilbert modular orbifold for the field $\mathbb{Q}(\sqrt{5})$   In this article we study the period map for a family of $K3$ surfaces which
is given by the anticanonial divisor of a toric variety. We determine the
period differential equation and its monodromy group. Moreover we show the
exact relation between our period differential equation and the unifomizing
differential equation of the Hilbert modular orbifold for the field
$\mathbb{Q}(\sqrt{5})$.

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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: eess