Abstract
An effective solution of the problem of analytic classification of plane branches is given. A finite stratification of any given equisingularity class of plane branches is determined and normal forms for each stratum are exhibited in such a way that two branches in normal form are easily recognized to be analytically equivalent or not. In this way, we solve the main problems proposed by O. Zariski (Le problème des modules pour les branches planes. Course given at the Centre de Mathématiques de L'École Polytechnique, Paris, October–November 1973).
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