论文标题
关于二维雅各布的猜想：Magnus的公式重新审视，我
On the two-dimensional Jacobian conjecture: Magnus' formula revisited, I
论文作者
论文摘要
令$ k $为特征0的代数封闭字段。 $ f，g \ in K [x，y] $，Magnus的公式[A。 Magnus，在几个复杂变量中保留转换的体积，Proc。阿米尔。数学。 Soc。 5（1954），256--266]描述了同质学位$ f_i $'s和$ g_i $'s之间的关系。我们展示了Magnus公式的更一般版本，并证明了二维Jacobian猜想作为其应用的特殊情况。
Let $K$ be an algebraically closed field of characteristic 0. When the Jacobian $({\partial f}/{\partial x})({\partial g}/{\partial y}) - ({\partial g}/{\partial x})({\partial f}/{\partial y})$ is a constant for $f,g\in K[x,y]$, Magnus' formula from [A. Magnus, Volume preserving transformations in several complex variables, Proc. Amer. Math. Soc. 5 (1954), 256--266] describes the relations between the homogeneous degree pieces $f_i$'s and $g_i$'s. We show a more general version of Magnus' formula and prove a special case of the two-dimensional Jacobian conjecture as its application.
