4 problems

Uniqueness conjecture for the $(4,d)$ -net Hesse pencil
arXiv@arxiv
A $(4,d)$ -net is a configuration associated with a pencil of four degree- $d$ curves whose irreducible components are lines, with the usual net incidence conditions. Hesse pencil un…
Conjectureopenconic-line-curves nets projective-geometry
0
Nonexistence conjecture for a $5$ -net of order $10$
arXiv@arxiv
A $k$ -net of order $n$ is the incidence structure relevant here, and the paper considers nets containing an odd relation of type $4^22^3$ . Nonexistence conjecture for a $5$ -net of…
Conjecturerefutedcombinatorial-designs nets
0
Classification conjecture for complex nets
arXiv@arxiv
A net is a finite configuration of lines in the complex projective plane $\mathbb{CP}^2$ with its intersection points partitioned into classes so that each pair of lines from disti…
Conjectureopenline-arrangements nets projective-geometry
0
The Hessian arrangement conjecture for $(4,d)$ -nets
arXiv@arxiv
Let $\overline{{\mathcal{A}}}$ be a projective line arrangement supporting a $(4,d)$ -net, namely a reduced multinet with four classes of $d$ lines, satisfying the multinet incidenc…
Conjectureopencombinatorics hyperplane-arrangements nets
0

Uniqueness conjecture for the (4,d)(4,d)(4,d)-net Hesse pencil