一类曲线的定义域(英文)

Fields of definition of a family of curves

设K为代数闭域k的有限生成扩域.C:f(x)=ayn为K上曲线,其中f是k上至少有3个单零点的多项式且n>3是正整数,n不是域k的特征的倍数,再设a■Kn,那么曲线C不能定义在k上,即曲线C:(x)=ayn不会k(a)同构于一条k上的曲线.

Let K be a finitely generated field extension of an algebraically closed field k and C ： f（x） = ayn be a curve over K, where char（k） n, f（x） E k [ x ]. When n 〉I 4, a ￠ Kn and f has at least three simple zeros, the curve C is not defined over k.