Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ordinary lines in space   We prove that if a finite point set in real space does not have too many
points on a plane, then it spans a quadratic number of ordinary lines. This
answers the real case of a question of Basit, Dvir, Saraf, and Wolf. It shows
that there is a significant difference in terms of ordinary lines between
planar point sets, which may span a linear number of ordinary lines, and truly
three-dimensional point sets. Our proof uses a projection argument of Kelly
combined with a theorem of Beck on the number of spanned lines of a planar
point set.

17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th