5 problems

Specialness criterion. The system $\mathcal L$ is special if and only if at least one of the following holds:

Simis' reformulation. The map $F$ is a Cremona map if and only if the Rees algebra $S[Iz]$ is normal.

Let $\pi:X\to S$ be a standard conic bundle, and suppose that there is a birational map … A Cremona transformation is a birational self-map of $\mathbb{P}^3$. Kantor's conjecture.…

A congruence of curves in $\mathbb{P}^3$ is an irreducible two-dimensional family of curves covering $\mathbb{P}^3$; its index is the number of curves through a general point. Kant…

Let $X$ be the blowup of $\mathbb{P}^2$ at $n$ sufficiently general points, and let $\mathcal{Q}_n$ and $\Delta_n^{\preccurlyeq}$ be as defined in the source. Strong Delta-conjectu…