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

Abstract

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.