RT info:eu-repo/semantics/article
T1 Properness and inversion of rational parametrizations of surfaces
A1 Pérez Díaz, Sonia
A1 Schicho, Josef
A1 Sendra Pons, Juan Rafael
K1 Proper rational parametrization
K1 Parametrization inverse
K1 Unirrationality
K1 Matemáticas
K1 Mathematics
AB In this paper we characterize the properness of rational parametrizations of hypersurfaces by means of the existence of intersection points of some additional algebraic hypersurfaces directly generated from the parametrization over a field of rational functions. More precisely, if V is a hypersurface over an algebraically closed field ? of characteristic zero and is a rational parametrization of V, then the characterization is given in terms of the intersection points of the hypersurfaces defined by x i q i (t¯)−p i (t¯), i=1,...,n over the algebraic closure of ?(V). In addition, for the case of surfaces we show how these results can be stated algorithmically. As a consequence we present an algorithmic criteria to decide whether a given rational parametrization is proper. Furthermore, if the parametrization is proper, the algorithm also computes the inverse of the parametrization. Moreover, for surfaces the auxiliary hypersurfaces turn to be plane curves over ?(V), and hence the algorithm is essentially based on resultants. We have implemented these ideas, and we have empirically compared our method with the method based on Gröbner basis.
PB Springer
SN 0938-1279
YR 2002
FD 2002
LK http://hdl.handle.net/10017/49638
UL http://hdl.handle.net/10017/49638
LA eng
DS MINDS@UW
RD 07-jun-2023