On the Structure of μ-Classes

Abstract

We prove that, if , then every rational parametrization of degree n and class μ is a limit of parametrizations of the same degree and class μ + 1. This property was conjectured in Cox, D., Sederberg, T., Chen, F. [Cox, D., Sederberg, T., Chen, F. (1998b)] and its validity allows an explicit description of the variety of parametrizations of degree n and class μ, for all (n, μ).

Key Words:

• Rational curves
• Parametrizations
• μ-Bases

Acknowledgments

I would like to thank David Cox for his careful reading of the manuscript and many helpful suggestions. This research was conducted while I was a postdoctoral fellow at the Institut National de Recherche en Informatique et en Automatique (INRIA) in Sophia-Antipolis, France, partially supported by Action A00E02 of the ECOS-SeTCIP French-Argentina bilateral collaboration.

Notes

^#Communicated by L. Ein.