ON A TROPICAL VERSION OF THE JACOBIAN CONJECTURE

Grigoriev, Dima; Radchenko, Danylo

Document type :

Communication dans un congrès avec actes

Title :

ON A TROPICAL VERSION OF THE JACOBIAN CONJECTURE

Author(s) :

Grigoriev, Dima [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Radchenko, Danylo [Auteur]
Max Planck Institute for Mathematics [MPIM]

Conference title :

MEGA 2019 - International Conference on Effective Methods in Algebraic Geometry

City :

Madrid

Country :

Espagne

Start date of the conference :

2019-06-17

Publication date :

2019

HAL domain(s) :

Informatique [cs]
Informatique [cs]/Géométrie algorithmique [cs.CG]

English abstract : [en]

We prove that, for a tropical rational map if for any point theconvex hull of Jacobian matrices at smooth points in a neighborhood of thepoint does not contain singular matrices then the map is an isomorphism. Wealso show ...
Show more >We prove that, for a tropical rational map if for any point theconvex hull of Jacobian matrices at smooth points in a neighborhood of thepoint does not contain singular matrices then the map is an isomorphism. Wealso show that a tropical polynomial map on the plane is an isomorphism ifall the Jacobians have the same sign (positive or negative). In addition, for atropical rational map we prove that if the Jacobians have the same sign andif its preimage is a singleton at least at one regular point then the map is anisomorphism.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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