Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Newton Non-degenerate Foliations and Blowing-ups   A codimension one singular holomorphic foliation is Newton non-degenerate if
it satisfies the classical conditions of Kouchnirenko and Oka, in terms of its
Newton polyhedra system. In this paper we prove that a foliation is Newton
non-degenerate if and only if it admits a logarithmic reduction of
singularities of a combinatorial nature.

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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin