Semigroup of two irreducible algebroid plane curves (Q1068147)

Let \(f_ 1,...,f_ n\) be n irreducible series in K[[X,Y]] (with K an algebraically closed field of arbitrary characteristic) and \(S(f_ 1,..,f_ n)\) the semigroup associated to \(f_ 1,...,f_ n\), i.e. the set of intersection vectors \((I(f_ 1,h),...,I(f_ n,h))\), where h runs over all algebroid plane curves which do not have \(f_ 1,...,f_ n\) as branches. The purpose of the paper under review is to solve the following two problems: (1) If one fixes two semigroups F and G associated to irreducible algebroid curves, determine all intersections I(f,g), with f and g irreducible series such that \(S(f)=F\) and \(S(g)=G\). - (2) Determine explicitly S(f,g) as a function of S(f), S(g) and I(f,g). (A result of Waldi - which is not constructive - shows that this last fact is always possible.)