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Mathematics, Algebraic Geometry
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.
