Say I have some projective space $\mathbb{P}^n$ and some line bundle $L=\mathcal{O}(-k)$. Now, I want to have a subvariety $Y$ in $\mathbb{P}^n$ such that $L\vert_Y$ is trivial.
When is this the case? I can only think of trivial solutions, like when $Y$ is just a point and I can't seem to find a standard treatment of this in literature