Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planes in cubic fourfolds   We show that the maximal number of planes in a complex smooth cubic fourfold
in ${\mathbb P}^5$ is $405$, realized by the Fermat cubic only; the maximal
number of real planes in a real smooth cubic fourfold is $357$, realized by the
so-called Clebsch--Segre cubic. Altogether, there are but three (up to
projective equivalence) cubics with more than $350$ planes.

12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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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: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas