I just can't figure out how to solve this problem.
"Let $S=Z(xy-zw)\subset \mathbb{P}^3$ and $l \subset S$ a line. Show that does not exist any surface $S'\subset \mathbb{P}^3$ such that $S\cap S'=l$."
Thank you so much for the help
I just can't figure out how to solve this problem.
"Let $S=Z(xy-zw)\subset \mathbb{P}^3$ and $l \subset S$ a line. Show that does not exist any surface $S'\subset \mathbb{P}^3$ such that $S\cap S'=l$."
Thank you so much for the help
Such a surface would have some positive degree $d$. What's the degree of $S$? So what would that make the degree of $S \cap S'$? This produces your contradiction. (At least, provided we are interpreting the equation $S \cap S' = l$ scheme-theoretically.)