ON A TROPICAL VERSION OF THE JACOBIAN CONJECTURE

Grigoriev, Dima; Radchenko, Danylo

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

ON A TROPICAL VERSION OF THE JACOBIAN CONJECTURE

Author(s) :

Grigoriev, Dima [Auteur]
Centre National de la Recherche Scientifique [CNRS]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Radchenko, Danylo [Auteur]

Journal title :

Journal of Symbolic Computation

Publisher :

Elsevier

Publication date :

2020

ISSN :

0747-7171

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We prove that, for a tropical rational map 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 more >We prove that, for a tropical rational map 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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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