ABSTRACT

Let $n\ge 2$.
Then a subset $C$ of the complex projective plane is a smooth algebraic curve
of degree $n$ iff the following conditions hold:

1. $C$ is closed and non empty.

2. Every line cuts $C$ in at most $n$ points.

3. For each $x\in C$ almost all lines through $x$ cut $C$ in exactly $n$
   points.