  Two algebroid branches are said to be equivalent if they have the same
multiplicity sequence. It is known that two algebroid branches $R$ and $T$ are
equivalent if and only if their Arf closures, $R'$ and $T'$ have the same value
semigroup, which is an Arf numerical semigroup and can be expressed in terms of
a finite set of information, a set of characters of the branch.
  We extend the above equivalence to algebroid curves with $d>1$ branches. An
equivalence class is described, in this more general context, by an Arf
semigroup, that is not a numerical semigroup, but is a subsemigroup of $\mathbb
N^d$. We express this semigroup in terms of a finite set of information, a set
of characters of the curve, and apply this result to determine other curves
equivalent to a given one.
