Let $k$ Be an infinite field.
Show that for any $n>3$ there exists a degree $n$ hypersurface $f(x_0, x_1, x_2, x_3)$, so deg$f = n$, that contains no lines.
I’ve been trying to figure this out / have been looking for a proof of this statement for a week now but no luck. Does anyone have a proof for this?
