=ADD=
=reftype=
14
=number=
01-19
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2001/01-19.ps.gz
=year=
2001
=month=
10
=author=
Sendra; J. Rafael
=title=
Normal Parametrizations of Algebraic Plane Curves over Fields of Characteristic Zero
=abstract=
In this paper we present a  theoretical and algorithmic analysis on the normality of 
rational parametrizations of algebraic plane curves over arbitrary fields of characteristic zero. If the field is algebraically closed we give an algorithm to decide whether a parametrization is proper and, if not, a normal parametrization is computed. If the field is not  algebraically closed the problem is more complecated, degenerated situation may appear. We classify the degenerations in strong and weak degenerations, and 
an algorithm to decide this phenomenon is derived. Furthermore, we prove that if the parametrization is strongly degenerated then the curve can not be normally parametrized, but weak degenerations can be resolved, and an algorithm to reparametrized the input weakly degenerated parametrization into a normal one is given. In addition, we show how these results can be applied and improved to the case of real rational curves.
=sponsor=
Partially supported by DGES PB98-0713-C02-01 and DGES HU1999-0029.
=keywords=
rational parametrization