RT info:eu-repo/semantics/article T1 Behavior of the fiber and the base points of parametrizations under projections A1 Pérez Díaz, Sonia A1 Sendra Pons, Juan Rafael K1 Rational parametrization K1 Unirational variety K1 Degree of a rational map K1 Fiber of a rational map K1 Base points K1 Generalized resultants K1 Ciencia K1 Matemáticas K1 Science K1 Mathematics AB Given a rational parametrization P( t ), t = (t1, . . . , tr ), of an r-dimensional unirational variety, weanalyze the behavior of the variety of the base points of P( t ) in connection to its generic fibre, when successivelyeliminating the parameters ti . For this purpose. we introduce a sequence of generalized resultants whose primitiveand 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 curvesand surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the correspondingGröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position andradical. PB Springer SN 1661-8270 YR 2013 FD 2013 LK http://hdl.handle.net/10017/20450 UL http://hdl.handle.net/10017/20450 LA eng NO This is the author’s version of a work that was accepted for publicationin Mathematics in Computer Science.Changes resulting from the publishing process, such as peer review,editing, corrections, structural formatting, and other quality controlmechanisms may not be reflected in this document.Changes may have been made to this work since it was submitted forpublication. A definitive version was subsequently publishedin Mathematics in Computer Science Volume 7, Issue 2 (2013), Page167-184 DOI 10.1007/s11786-013-0139-8 NO Both authors are members of the of the Research Group ASYNACS (Ref. CCEE2011/R34). NO Ministerio de Ciencia e Innovación DS MINDS@UW RD 29-mar-2024