9 problems

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…

Let $d\geq 4$ be even, and consider a special Cremona transformation of type $(2,d)$ with center $X\subset\mathbb{P}^N$, where $X$ has dimension $n$ and the associated secant-defec…

Let $f^{(r)}$ be a sub-Hankel determinant, and let $J$ denote its full Jacobian ideal, generated by the partial derivatives of $f^{(r)}$. An ideal is of linear type if its Rees alg…

Cremona-normal form conjecture. Up to a Cremona transformation of the plane, one can assume that $D_{11}$ is irreducible, has an ordinary point of multiplicity $d-2$ at $p$, and ha…

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 $\overline{X}(r+1,3,3)\subset\mathbb P^{2r+3}$ be a variety of the indicated type, let $\mathbb J$ be a cubic Jordan algebra of dimension $r+1$, and let a quadro-quadratic Crem…

Let $\mathbb J$ be a complex, cubic, unitary Jordan algebra, and let $X_{\mathbb J}\subset \operatorname{\mathbb P}^{2n+1}$ be the associated twisted cubic, where…