Reduccion del grado en aplicaciones de Keller

Abstract

The polynomial maps whose Jacobian determinant is equal to 1 are called Keller maps. The Keller Jacobian conjecture claims that every Kellermap is injective. This conjecture is true for polynomials whose degree is less than or equal to two. In this paper we prove that the general casereduces to the study of the injectivity of maps of the form z 7! z+H(z),where the nonzero components of H are homogeneous polynomials of degree three, and every Jacobian matrix DH(z) is nilpotent.