Timeline for Subset of a complex manifold whose intersection with every holomorphic curve is analytic

8 events

when toggle format	what		by	license	comment
May 6 at 19:11	history	edited	Francesco Polizzi	CC BY-SA 4.0	deleted 9 characters in body
May 6 at 18:59	history	edited	Francesco Polizzi	CC BY-SA 4.0	added 102 characters in body
May 6 at 18:49	comment	added	Francesco Polizzi		"Of course" in which sense? Osgood's theorem is about lines, so how could one guess that you were talking about germs? After your update, my answer looks wrong, while it was correct when I wrote it. I think you should have asked another question rather than updating yours after my answer was posted. Anyway, it does not matter...
May 6 at 17:08	comment	added	V. Rogov		One can also assume that $X$ is algebraic and ask if it is true that $A \cap C$ is an algebraic subset of $C$ for an algebraic curve $C \subset X$ if and only if $A$ is an algebraic subvariety. But I guess this is a completely different question.
May 6 at 17:05	comment	added	V. Rogov		Of course, I did not assume to test only on the closed curves. The question is local, so you can test on germs of curves (essentially on disks). I added an update to the post.
May 6 at 14:32	history	edited	Francesco Polizzi	CC BY-SA 4.0	added 484 characters in body
May 6 at 14:27	history	edited	Francesco Polizzi	CC BY-SA 4.0	added 484 characters in body
May 6 at 14:09	history	answered	Francesco Polizzi	CC BY-SA 4.0