2 problems

Let $\mathbb{F}$ be a field, let $n\geq 3$, and let $\mathfrak{L}$ be a finite collection of $L$ lines in $\mathbb{F}^n$. For each joint $x\in J(\mathfrak{L})$, let $N(x)$ be the n…

Let $\mathfrak{L}_1,\ldots,\mathfrak{L}_n$ be transversal collections of $L_1,\ldots,L_n$ lines in $\mathbb{F}^n$, meaning that whenever $n$ lines, one from each collection, meet a…