Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
Think about degrees. – Andrew Oct 21 '12 at 21:06
up vote 2 down vote accepted

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.)

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.