Fully simple singularities of plane and space curves

In this work we introduce the definition of fully simple singularities of parameterized curves and explain that this definition is more natural than the definition of simple singularities. The set of fully simple singularities is much smaller than the set of simple ones. We determine and classify all fully simple singularities of plane and space curves, with any number of components. Our classification results imply that any fully simple singularity of a plane or a space curve is quasi-homogeneous (whereas there is a number of non-quasi-homogeneous simple singularities). Another outcome of our classification results is a one-to-one correspondence between the fully simple singularities of plane curves and the classical A-D-E singularities of functions.