2003/02/19 by Valentina Barucci, Marco D'Anna, Ralf Froberg
Mathematics · #math.AC #math.AG #msc:13H15 #msc:14B05
published as Lecture Notes Pure Appl. Math. 231 (2003), 37-50 · 14 pages
arxiv created 2003/02/19 · arxiv updated 2009/11/30
Two plane analytic branches are topologically equivalent if and only if they have the same multiplicity sequence. We show that having same semigroup is equivalent to having same multiplicity sequence, we calculate the semigroup from a parametrization, and we characterize semigroups for plane branches. These results are known, but the proofs are new. Furthermore we characterize multiplicity sequences of plane branches, and we prove that the associated graded ring, with respect to the values, of a plane branch is a complete intersection.