2002/04/30 by Carlos D'Andrea
Mathematics · #math.AG #math.AC #msc:13Pxx #msc:14H50
published as Communications in Algebra, Vol. 32, No.1 159-165, 2004. · 6 pages, revised version accepted for publication in Communications in Algebra
arxiv created 2002/09/06 · arxiv updated 2009/11/30
We prove that, if μ<\lfloor n/2\rfloor, then every rational plane curve of degree n and class μis a limit of parametrizations of the same degree and class μ+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 μ, for all (n,μ).