Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The two-dimensional Jacobian conjecture and the lower side of the Newton
  polygon   We prove that if the Jacobian Conjecture in two variables is false and (P,Q)
is a standard minimal pair, then the Newton polygon HH(P) of P must satisfy
several restrictions that had not been found previously. This allows us to
discard some of the corners found in [GGV, Remark 7.14] for HH(P), together
with some of the infinite families found in [H, Theorem~2.25]

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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin