Projection from a point on a plane curve
= Projection from a point on a plane curve
For a degree-$d$ plane curve $C$ and a smooth point $p\in C$, the pencil of lines through $p$ induces a morphism $C\to\mathbb P^1$. A general line has one fixed intersection at $p$, so <Bézout theorem> makes the morphism have degree $d-1$.