Timeline for Curve meeting an open subset

5 events

when toggle format	what		by	license	comment
Oct 8, 2015 at 15:07	comment	added	roy smith		mathoverflow.net/questions/62843/… the actual reference to a paper of C.P. Ramanujam is in a comment to an answer.
Oct 7, 2015 at 9:13	comment	added	Jason Starr		There is a reference near the beginning of Chapter II, "Algebraic Theory via Varieties", of Mumford's "Abelian Varieties", the Lemma on p. 56. This is one step in the proof of the Theorem of the Cube.
Oct 7, 2015 at 8:01	comment	added	Jérémy Blanc		I need $\Gamma$ irreducible (a priori the component touching $p$ could be outside of $U$). When $X$ is smooth, this follows from Bertini. In general, is it true also?
Oct 7, 2015 at 7:58	comment	added	Francesco Polizzi		Maybe I'm missing something, but why do you need the smoothness of $X$? It seems to me that, in any case, the hyperplane argument gives a curve $\Gamma$ with the required properties. Just take a projective closure $\bar X$ of $X$, embed it in a projective space and start cutting with general hyperplanes through $p$. Since $U$ is dense in $X$, and hence in $\bar X$, these hyperplanes will meet $U$, so the same holds for their intersection. Maybe you want $\Gamma$ smooth?
Oct 7, 2015 at 7:18	history	asked	Jérémy Blanc	CC BY-SA 3.0