4 problems

Let $X\subset {\mathbb P}^N$ be covered by lines, let $x\in X$ be a general point, and let $\mathcal L_x\subset {\mathbb P}^{n-1}$ be the variety of lines through $x$. Local-to-glo…

Let $X\subset {\mathbb P}^N$ be covered by lines, let $x\in X$ be a general point, and let $\mathcal L_x\subset {\mathbb P}^{n-1}$ be the variety of lines through $x$. Let $T$ be t…

Let $X\subset \mathbb{P}^{N}$ be a non-degenerate variety covered by lines. Write $n=\dim(X)$ and $c=\operatorname{codim}(X)$, and let $a$ denote the dimension of the family of lin…

Let $X\subset\mathbb{P}^N$ be a smooth irreducible non-degenerate variety of dimension $n$ covered by lines. For a general point $x\in X$, let…