Arf characters of an algebroid curve

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 generalcontext, by an Arf semigroup, that is not a numerical semigroup, but is a subsemigroup of 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.