Analytic classification of plane branches up to multiplicity 4

Abstract: We perform the analytic classification of plane branches of multiplicity less than or equal to four. This is achieved by computing a Standard Basis for the modules of Kähler differentials of such branches by means of the algorithm developed in [Hefez, A., Hernandes, M.E., 2007a. Standard bases for local rings of branches and their module of differentials. J. Symbolic Comput. 42, 178–191] and then applying the classification method for plane branches given in [Hefez, A., Hernandes, M.E., 2007b. The analytic classification of plane branches. arXiv:0707.4502]. [Copyright &y& Elsevier]