I will point out that the tag (geometry) is deprecated on MathOverflow, see
the tag-info. Perhaps the tag can be simple omitted or some more suitable tags can be used for the question. (Since this is not an area of mathematics I am familiar with, I'd decided not to edit the tags myself and leave comments instead.) —
Martin Sleziak 41 secs ago
Let X be a nonsingular threefold of degree d contained in $\mathbb{P}^4$ and let P be a point on X. Is it possible to find a plane H contained in $T_P (X)$ such that $X \cap H$ is not a union of d lines?
