Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the geometry of real or complex supersolvable line arrangements   Given a rank 3 real arrangement $\mathcal A$ of $n$ lines in the projective
plane, the Dirac-Motzkin conjecture (proved by Green and Tao in 2013) states
that for $n$ sufficiently large, the number of simple intersection points of
$\mathcal A$ is greater than or equal to $n/2$. With a much simpler proof we
show that if $\mathcal A$ is supersolvable, then the conjecture is true for any
$n$ (a small improvement of original conjecture). The Slope problem (proved by
Ungar in 1982) states that $n$ non-collinear points in the real plane determine
at least $n-1$ slopes; we show that this is equivalent to providing a lower
bound on the multiplicity of a modular point in any (real) supersolvable
arrangement. In the second part we find connections between the number of
simple points of a supersolvable line arrangement, over any field of
characteristic 0, and the degree of the reduced Jacobian scheme of the
arrangement. Over the complex numbers even though the Sylvester-Gallai theorem
fails to be true, we conjecture that the supersolvable version of the
Dirac-Motzkin conjecture is true.

20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics