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

Abstract

In this note we prove the relation between Betti numbers of an Arf semigroup $S$ and its blowup $S^{\prime }$ in the case when they have the same multiplicity $n$. The relation is then ${\beta }_{i,s}(S^{\prime })={\beta }_{i,s+(i+1)n}(S)$.

arXiv commentfinal version, 4 pages