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In this note we prove the relation between Betti numbers of an Arf semigroup S and its blowup S in the case when they have the same mul-tiplicity n. The relation is then β i,s (S) = β i,s+(i+1)n (S). Definition 1. 2. The smallest generator in G(S) is called the multiplicity of S and the number of elements in G(S) the embedding dimension of S. Remark 1.3. The multiplicity is greater or equal to embedding dimension. Entrato in redazione: 8 agosto 2011fatcat:nkmu577nhvaj7mgv37g4772qge