Bézoutians and injectivity of polynomial maps
In the paper under review, the author uses the multivariate Bézoutian to study polynomial morphisms. He proves that an endomorphism \(f\) is injective on rational points if its multivariate Bézoutian is constant and gives the relations between multivariate Bézoutian and the Jacobians of polynomial endomorphisms. In addition, he also proves an endomorphism \(f\) is injective at a given rational point iff its reduced Bézoutian is constant in the case that the determinate of the Jacobian of \(f\) is a nonzero constant.
scientific article; zbMATH DE number 7661183