Details:
Title  Behavior of the fiber and the base points of parametrizations under projections.  Author(s)  Sonia PerezDiaz, J. Rafael Sendra  Type  Article in Journal  Abstract  Given a rational parametrization (t⎯⎯),t⎯⎯=(t1,…,tr) , of an rdimensional unirational variety, we analyze the behavior of the variety of the base points of (t⎯⎯) in connection to its generic fibre, when successively eliminating the parameters t i . 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 t 1general position and radical.  Keywords  Rational parametrization, Unirational variety, Degree of a rational map, Fiber of a rational map, Base points, Generalized resultants  ISSN  16618270; 16618289/e 
URL 
http://link.springer.com/article/10.1007%2Fs1178601301398 
Language  English  Journal  Math. Comput. Sci.  Volume  7  Number  2  Pages  167184  Publisher  Springer (Birkh\"auser), Basel  Year  2013  Edition  0  Translation 
No  Refereed 
No 
