Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rank two affine submanifolds in $\mathcal{H}(2,2)$ and
  $\mathcal{H}(3,1)$   We classify all rank two affine manifolds in strata in genus three with two
zeros. This confirms a conjecture of Maryam Mirzakhani in these cases. Several
technical results are proven for all strata in genus three, with the hope that
they may shed light on a complete classification of rank two manifolds in genus
three.

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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin