2003/01/31 by Valentina Barucci, Barucci, Valentina, Marco D'Anna +3
Mathematics · #13H15 #14B05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13H15 #msc:14B05
paper · pdf · doi:10.48550/arxiv.math/0301366
17 pages
arxiv created 2003/06/11 · arxiv updated 2009/11/30
Two algebroid branches are said to be equivalent if they have the same multiplicity sequence. It is known that two algebroid branches R and T are equivalent if and only if their Arf closures, R' and T' have the same value semigroup, which is an Arf numerical semigroup and can be expressed in terms of a finite set of information, a set of characters of the branch. We extend the above equivalence to algebroid curves with d>1 branches. An equivalence class is described, in this more general context, by an Arf semigroup, that is not a numerical semigroup, but is a subsemigroup of \mathbb Nd. We express this semigroup in terms of a finite set of information, a set of characters of the curve, and apply this result to determine other curves equivalent to a given one.