Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Products of pairs of Dehn twists and maximal real Lefschetz fibrations   We address the problem of existence and uniqueness of a factorization of a
given element of the modular group into a product of two Dehn twists. As a
geometric application, we conclude that any maximal real elliptic Lefschetz
fibration is algebraic.

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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci