%0 Journal Article
%T Jacobian Conjecture and Nilpotency
%A Elzbieta Adamus
%A Pawel Bogdan
%A Teresa Crespo
%A Zbigniew Hajto
%J Mathematics
%D 2015
%I arXiv
%X For K a field of characteristic 0 and d any integer number greater than or equal to 2, we prove the invertibility of polynomial endomorphisms of the affine space of dimension d over K of the form F=Id+H, where each coordinate of H is the cube of a linear form and the cube of the Jacobian matrix of H is equal to zero. Our proof uses the inversion algorithm for polynomial maps presented in our previous paper. Our current result leads us to formulate a conjecture relating the nilpotency degree of the Jacobian matrix of H with the number of necessary steps in the inversion algorithm.
%U http://arxiv.org/abs/1508.02012v1