RT info:eu-repo/semantics/article
T1 A first approach towards normal parametrizations of algebraic surfaces
A1 Pérez Díaz, Sonia
A1 Sendra Pons, Juan Rafael
A1 Villarino Cabellos, Carlos
K1 Rational surface
K1 Normal parametrizations
K1 Surjectivity
K1 Normality of a rational parametrization
K1 Pseudo-normal parametrization
K1 Matemáticas
K1 Mathematics
AB In this paper we analyze the problem of deciding the normality (i.e. thesurjectivity) of a rational parametrization of a surface S. The problem canbe approached by means of elimination theory techniques, providing a properclose subset Z ⊂ S where surjectivity needs to be analyzed. In general, thesedirect approaches are unfeasible because Z is very complicated and its elements computationally hard to manipulate. Motivated by this fact, we studyad hoc computational alternative methods that simplifies Z. For this goal,we introduce the notion of pseudo-normality, a concept that provides necessary conditions for a parametrization for being normal. Also, we provide analgorithm for deciding the pseudo-normality. Finally, we state necessary andsufficient conditions on a pseudo-normal parametrization to be normal. As aconsequence, certain types of parametrizations are shown to be always normal. For instance, pseudo-normal polynomial parametrizations are normal.Moreover, for certain class of parametrizations, we derive an algorithm fordeciding the normality.
PB World Scientific
SN 0218-1967
YR 2010
FD 2010-12
LK http://hdl.handle.net/10017/49610
UL http://hdl.handle.net/10017/49610
LA eng
NO Ministerio de Ciencia e Innovación
DS MINDS@UW
RD 03-jun-2023