%0 Journal Article
%A Pérez Díaz, Sonia
%A Sendra Pons, Juan Rafael
%A Villarino Cabellos, Carlos
%T A first approach towards normal parametrizations of algebraic surfaces
%D 2010
%@ 0218-1967
%U http://hdl.handle.net/10017/49610
%X In this paper we analyze the problem of deciding the normality (i.e. the
surjectivity) of a rational parametrization of a surface S. The problem can
be approached by means of elimination theory techniques, providing a proper
close subset Z ⊂ S where surjectivity needs to be analyzed. In general, these
direct approaches are unfeasible because Z is very complicated and its elements computationally hard to manipulate. Motivated by this fact, we study
ad 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 an
algorithm for deciding the pseudo-normality. Finally, we state necessary and
sufficient conditions on a pseudo-normal parametrization to be normal. As a
consequence, 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 for
deciding the normality.
%K Rational surface
%K Normal parametrizations
%K Surjectivity
%K Normality of a rational parametrization
%K Pseudo-normal parametrization
%K Matemáticas
%K Mathematics
%~ Biblioteca Universidad de Alcala