On the relation between Betti numbers of an Arf semigroup and its blowup

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 multiplicity $n$. The relation is then $β_{i,s}(S')=β_{i,{s+(i+1)n}}(S)$.

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