Let $f:\mathbb{P}^{n}\longrightarrow \mathbb{P}^{m}$ be a morphism with $n>m$, where $\mathbb{P}^{n}$ denote the $k$-proyective $n$-space with $k$ an algebraic closed field with characteristic $0$. Prove that the image of $f$ consist of only one point.
If $V=Im(f)$ I think we can show that the ideal generated by $V$, $\mathbb{I}(V)$ is maximal, or equivalently showing that $k[x_{0},...,x_{m}]/\mathbb{I}(V)$ is a field, but I don't see how to prove this.
Also, the excercise don't say what tipe of morphism is $f$ so I'm assuming is a morphism of projective varieties.
Any help will be appreciated! Thank you.
