Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lines on $p$-adic and real cubic surfaces   We study lines on smooth cubic surfaces over the field of $p$-adic numbers,
from a theoretical and computational point of view. Segre showed that the
possible counts of such lines are $0,1,2,3,5,7,9,15$ or $27$. We show that each
of these counts is achieved. Probabilistic aspects are also investigated by
sampling both $p$-adic and real cubic surfaces from different distributions and
estimating the probability of each count. We link this to recent results on
probabilistic enumerative geometry. Some experimental results on the Galois
groups attached to $p$-adic cubic surfaces are also discussed.

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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom