3
$\begingroup$

Dear colleagues,

Could you give me a reference (not a proof:) to the following folklore result. If $X\subset\mathbb P^n$ is a smooth irreducible projective variety of dimension $>1$, then any hyperplane section of $X$ is connected. The base field is algebraically closed, characteristic is arbitrary.

Thank you in advance, Serge

$\endgroup$
6
  • 1
    $\begingroup$ en.wikipedia.org/wiki/… $\endgroup$ May 18, 2013 at 17:33
  • $\begingroup$ @Vivek. Wow, I had now idea that even this is on Wiki:) Thanks, I will look up the paper. $\endgroup$ May 18, 2013 at 17:45
  • 3
    $\begingroup$ The Fulton-Hansen theory is more general, but this particular case is the Lemma of Enriques-Severi-Zariski, which is older. $\endgroup$ May 18, 2013 at 18:40
  • $\begingroup$ @jason. Thanks! Could you give an explicit reference? $\endgroup$ May 18, 2013 at 18:50
  • 4
    $\begingroup$ ( Hartshorne, Algebraic Geometry, Springer, GTM 52, Cor. 7.9, p. 244 ) $\endgroup$ May 19, 2013 at 6:35

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.