Type: Article

Jacobian mates for non-singular polynomial maps in Cn with one-dimensional fibers

Bustinduy, Alvaro; Giraldo, Luis; Muciño-Raymundo, Jesús;

Abstract:

Let F=(F2,…,Fn):Cn?Cn?1 be a non-singular polynomial mapping, i.e., rank(Jac(F2,…,Fn))=n?1 everywhere in Cn. The authors give a sufficient condition under which there exists a polynomial F1 such that (F1,…,Fn):Cn?Cn is a Keller mapping, i.e., det(Jac(F1,…,Fn))=const?0. This condition has three items: (1) the union of reducible fibers F?1(c) forms an algebraic subset of Cn of codimension at least 2, (2) a form constructed of F is exact on fibers of F, (3) there is a finite set Y in the hyperplane at infinity H? of CPn such that the projective closure of each fiber F?1(c) in CPn adds points of Y to F?1(c).