%0 Journal Article 
%A Pérez Díaz, Sonia
%A Sendra Pons, Juan Rafael
%T Behavior of the fiber and the base points of parametrizations under projections
%D 2013
%@ 1661-8270
%U http://hdl.handle.net/10017/20450
%X Given a rational parametrization P( t ), t = (t1, . . . , tr ), of an r-dimensional unirational variety, we
analyze the behavior of the variety of the base points of P( t ) in connection to its generic fibre, when successively
eliminating the parameters ti . For this purpose. we introduce a sequence of generalized resultants whose primitive
and content parts contain the different components of the projected variety of the base points and the fibre.
In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves
and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding
Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and
radical.
%K Rational parametrization
%K Unirational variety
%K Degree of a rational map
%K Fiber of a rational map
%K Base points
%K Generalized resultants
%K Ciencia
%K Matemáticas
%K Science
%K Mathematics
%~ Biblioteca Universidad de Alcala