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arXiv · 2005.09797

B\'ezoutians and injectivity of polynomial maps

Stephen McKean
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Abstract

We prove that an endomorphism $f$ of affine space is injective on rational points if its B\'ezoutian is constant. Similarly, $f$ is injective at a given rational point if its reduced B\'ezoutian is constant. We also show that if the Jacobian determinant of $f$ is invertible, then $f$ is injective at a given rational point if and only if its reduced B\'ezoutian is constant.

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Stephen McKean. 2020-05-20. B\'ezoutians and injectivity of polynomial maps. https://doi.org/10.1016/j.jpaa.2022.107298

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