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Journal Article

On a tropical version of the Jacobian conjecture

MPS-Authors
/persons/resource/persons236038

Radchenko,  Danylo
Max Planck Institute for Mathematics, Max Planck Society;

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Fulltext (public)

arXiv:1902.07733.pdf
(Preprint), 104KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Grigoriev, D., & Radchenko, D. (in press). On a tropical version of the Jacobian conjecture. Journal of Symbolic Computation, Corrected Proof Online - Print pending. doi:10.1016/j.jsc.2020.07.012.


Cite as: http://hdl.handle.net/21.11116/0000-0007-E821-E
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.