4 problems

Levinson–Ullery conjecture. For $d\geq 1$, if

Let $\Gamma$ be a complete intersection of $n$ quadrics in $\mathbb{P}^n$. Let $X\subset\mathbb{P}^n$ be a hypersurface of degree $d$ containing a subscheme $\Omega\subset\Gamma$ w…

Plane configuration conjecture. If

Let $\Gamma$ be any subscheme of a zero-dimensional complete intersection of hypersurfaces of degrees $d_1\leq\dots\leq d_c$ in a projective space $P^c$. Say that $\Gamma$ fails to…