Verification of the Jacobian Conjecture for $d$-linear maps in two variables
Commutative Algebra
2021-11-23 v1 Algebraic Geometry
Combinatorics
Abstract
For any integer , we verify the Jacobian Conjecture for a -linear map in two variables. We prove that almost all the coefficients of the formal inverse are in the ideal specified by the Jacobian condition. We find expressions for certain elements in terms of the generators of this ideal. To obtain these expressions, we generalize a bijective proof of the Cayley-Hamilton theorem in two ways.
Keywords
Cite
@article{arxiv.2111.10739,
title = {Verification of the Jacobian Conjecture for $d$-linear maps in two variables},
author = {Mario DeFranco},
journal= {arXiv preprint arXiv:2111.10739},
year = {2021}
}