3 problems

Vatne's conjecture. There is a degree-two Cohen–Macaulay subscheme $Z$ such that

Let $X=\mathbb{P}^N\subset\mathbb{P}^{N+M}$ be a linear subspace of dimension $N\geq 6$. Let $W$ be a Cohen–Macaulay multiple monomial scheme with reduced subscheme…

Let $\mathbb{P}^N$ with $N\geq 6$ be a linear subspace of codimension two in $\mathbb{P}^{N+2}$. Let $M$ denote the integer occurring in the infinitesimal-neighbourhood notation, a…