Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial partitioning on varieties of codimension two and
  point-hypersurface incidences in four dimensions   We present a polynomial partitioning theorem for finite sets of points in the
real locus of an irreducible complex algebraic variety of codimension at most
two. This result generalizes the polynomial partitioning theorem on the
Euclidean space of Guth and Katz, and its extension to hypersurfaces by Zahl
and by Kaplan, Matou\v{s}ek, Sharir and Safernov\'a.
  We also present a bound for the number of incidences between points and
hypersurfaces in the four-dimensional Euclidean space. It is an application of
our partitioning theorem together with the refined bounds for the number of
connected components of a semi-algebraic set by Barone and Basu.

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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys