Bézoutians and injectivity of polynomial maps

Abstract

We prove that an endomorphism $f$ of affine space is injective on rational points if its Bézoutian is constant. Similarly, $f$ is injective at a given rational point if its reduced Bézoutian 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 Bézoutian is constant.

8 pages. Final version, but comments still welcome!

References in corpus (1)

• Some approaches toward the Jacobian conjecture