3 problems

Let ${\mathcal A}=\{H_1,\ldots,H_s\}$ be a generic collection of $s\geq n+1$ hyperplanes in $\mathbb P^n$, with defining linear forms $\ell_1,\ldots,\ell_s$. For $1\leq c\leq n$, l…

Let $cmathbb K$ be a field of characteristic $0$, let $cmathcal C=(cell_1,\ldots,cell_n)\subset R=cmathbb K[x_1,\ldots,x_k]$ be an $[n,k]$-linear code with no zero columns, and let…

Let $s>n$ and let $\mathcal H=\{H_1,\ldots,H_s\}$ be properly meeting hyperplanes in ${\bf P}^n$, defined by linear forms $L_i$. Let $N+1=s$, let $\mathcal H'$ be the coordinate hy…