$f(A(t),B(t))=0$ (where both series converge), and (ii) not both, $A$ and $B$, are constants. Then ${\cal P}=(A,B)$ is called an [*(affine) local parametrization*]{} of $\cal C$. Moreover, if $\ord(A),\ord(B)\geq 0$, the point ${\cal P}(0)=(a,b)\in {\cal C}$ is called the [*center*]{} of $\cal P$.

In the following, we deal with affine curves. The results and notions presented can be adapted for projective curves in an obvious way.

Two local parametrizations, ${\cal P}_1$ and ${\cal P}_2$, of an algebraic plane curve $\cal C$ are called [*equivalent*]{} if there exists $R\in {\Bbb C}[[t]]$, with $\ord(R)=1$, such that ${\cal P}_1 ={\cal
P}_2(R)$. It can be proved that this equivalence of local parametrizations is actually an equivalence relation.

If a local parametrization ${\cal P}$, or one equivalent, satisfies that ${\cal P}(t) = {\cal P}'(t^k)$ for some parametrization ${\cal P}'$ and for some natural number $k>1$, then ${\cal P}$ is said to be [*reducible*]{}. Otherwise, ${\cal P}(t)$ is said to be [*irreducible*]{}. Under these conditions, we introduce the notion of [*place*]{} as follows.

An equivalence class of irreducible local parametrizations of the algebraic plane curve $\cal C$ is called a [*place*]{} of $\cal C$. The common center of the local parametrizations (if it exists) is the 