5 problems

Uniqueness conjecture. The quartic surface discovered in the cited work is the only quartic that attains the bound of $52$ lines.

Quadric-configuration conjecture. Every double $2d$ on $X$ consists of $4d$ lines that are the union of two quadric configurations on $X$.

Absolute linear Harbourne constant conjecture. If $i\leqslant 2q-2$, then $H(d)=h(d)$, where

Let $s$ lines be given in the real projective plane, not all belonging to the same pencil through a fixed point. A point where three lines meet is a triple point, while a point whe…

Classification and ACM conjecture. Every finite set of lines in ${\mathbf P}^3$ has type $(d-1,d)$ if and only if it is coplanar or is the intersection of a finite set of hyperplan…