ON A TROPICAL VERSION OF THE JACOBIAN CONJECTURE
Résumé
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.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...