On the structure of mu-classes

Abstract

We prove that, if \mu<\lfloor n/2\rfloor, then every rational plane curve of degree n and class \mu is a limit of parametrizations of the same degree and class \mu+1. This property was conjectured in D.Cox, T.Sederberg,F.Chen's paper: "The moving line ideal basis of planar rational curves" (Comput. Aided Geom. Des. 15 (1998), 803-827), and its validity allows an explicit description of the variety of parametrizations of degree n and class \mu, for all (n,\mu).