Could anybody help me with the following question ?
Assume we are given:
(1) a finite order (linear) automorphism $g$ of the projective space $\mathbb{P}^r$,
(2) a closed algebraic subvariety $Z \subset \mathbb{P}^r$ of codimension at least 2.
Is it always possible to find a line in $\mathbb{P}^r$ which is stable under $g$ and does not meet $Z$?
Thanks in advance!