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 $\beta_{i,s}(S')=\beta_{i,{s+(i+1)n}}(S)$. 
Micha{\l} Laso\'n
math.AC math.GR