Let $X$ be a smooth, proper algebraic variety over a field $k$, of positive dimension.
Is it true that $X$ contains a smooth Zariskiclosed curve?
If it is projective, this is true by Bertini. But is it true in general?
Let $X$ be a smooth, proper algebraic variety over a field $k$, of positive dimension. Is it true that $X$ contains a smooth Zariskiclosed curve? If it is projective, this is true by Bertini. But is it true in general? 

