On a tropical version of the Jacobian conjecture
Algebraic Geometry
2019-02-22 v1
Abstract
We prove for a tropical rational map that if for any point the convex hull of Jacobian matrices at smooth points in a neighborhood of the point does not contain singular matrices then the map is an isomorphism. We also show that a tropical polynomial map on the plane is an isomorphism if all the Jacobians have the same sign (positive or negative). In addition, for a tropical rational map we prove that if the Jacobians have the same sign and if its preimage is a singleton at least at one regular point then the map is an isomorphism.
Keywords
Cite
@article{arxiv.1902.07733,
title = {On a tropical version of the Jacobian conjecture},
author = {Dima Grigoriev and Danylo Radchenko},
journal= {arXiv preprint arXiv:1902.07733},
year = {2019}
}