Jacobian Conjecture and Nilpotency
Algebraic Geometry
2015-08-11 v1
Abstract
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.
Cite
@article{arxiv.1508.02012,
title = {Jacobian Conjecture and Nilpotency},
author = {Elzbieta Adamus and Pawel Bogdan and Teresa Crespo and Zbigniew Hajto},
journal= {arXiv preprint arXiv:1508.02012},
year = {2015}
}