Poincar\'e series for plane curve singularities and their behaviour under projections

Our purpose is to investigate all defined Poincar'e series associated with multi-index filtrations and value semigroups of curve singularities—not necessarily complex—with regard to the property of forgetting variables, i.e., by making variables of the series to be 1. Generalised Poincar'e series of motivic nature will be also considered.