Morphism from the projective plane contracting a line
= Morphism from the projective plane contracting a line
Every morphism $f:\mathbb P^2\to\mathbb P^n$ satisfies $f^*\mathcal O(1)\cong\mathcal O(d)$ for some $d\geq0$. If $f$ contracts a line, restriction to that line makes $\mathcal O(d)$ trivial, hence $d=0$ and all defining sections are constant. Thus the entire morphism is constant.