论文标题
多项式图的贝祖特人和注射率
Bézoutians and injectivity of polynomial maps
论文作者
论文摘要
我们证明，如果其bézoutian恒定，仿射空间的内态$ f $是理性点。同样，如果$ f $减少的bézoutian是恒定的，则在给定的理性点上是注入的。我们还表明，如果jacobian的决定因素是$ f $是可逆的，那么$ f $在给定的理性点上是且仅当其减少的bézoutian是恒定的时。
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.
