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ON A TROPICAL VERSION OF THE JACOBIAN CONJECTURE

Abstract : 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.
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https://hal.inria.fr/hal-02912322
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Submitted on : Wednesday, August 5, 2020 - 4:14:25 PM
Last modification on : Wednesday, December 30, 2020 - 3:00:03 PM
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Dima Grigoriev, Danylo Radchenko. ON A TROPICAL VERSION OF THE JACOBIAN CONJECTURE. MEGA 2019 - International Conference on Effective Methods in Algebraic Geometry, Jun 2019, Madrid, Spain. ⟨hal-02912322⟩

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