Integral curves and Jacobian Conjecture

2023/04/28 by Charbonnel, Jean-Yves
#14A10 #14E05 #34A05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.14675

Abstract

In this note, we are interested in the Jacobian Conjecture. Following the results of L.M.~Dru\rm zkowski, we consider some vector fields depending on a certain étale polynomial map. From results of semialgebraic geometry with the consideration of some integral curves of these vector fields, we deduce that an étale polynomial endomorphism is a polynomial automorphism.

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