7 problems

Let $Z\subset\mathbb P^3$ be a set of at least $5$ points in linear general position, meaning that no $3$ points of $Z$ are collinear and no $4$ points are coplanar. Projection con…

Converse conjecture. Then

Inclusion-property conjecture. $X$ is arithmetically Cohen–Macaulay (ACM).

Triple-line conjecture. If

Let $C>0$ and let ${\mathcal P}\subset\mathbb R^D$ be a finite point set that is proper $D$-dimensional up to $C$. For $r<D$, let $S^{(r)}\subset\mathbb R^D$ range over affine subs…

Let ${\mathcal P}\subset\mathbb R^2$ be any finite point set, let $3\le k\le|{\mathcal P}|$, and let $C>0$. An intersection is proper 2-dimensional up to $C$ in the sense used by t…

Let ${\mathcal P}\subset\mathbb R^2$ be a finite point set. An isometry is a distance-preserving map $\varphi:\mathbb R^2\to\mathbb R^2$. The isometry overlap conjecture. There is…