关于全纯曲线的Milloux型不等式

Milloux type inequality on holomorphic curves

利用全纯曲线的导曲线,建立了全纯曲线的Milloux型不等式,证明了Picard型定理:设f是C到P^(n)(C)的一条全纯曲线,f是f的一条导曲线,{H_(j)}^(2n+1)_(j=1)是P^(n)(C)中一族处于一般位置的超平面,若f避开超平面族{H_(j)}^(n+1)_(j=1),f避开超平面族{H_(j)}^(2n+1)_(j=n+2),则f是一条常值曲线,其中H_(1),H_(2),…,H_(n+1)是n+1个坐标超平面。举例说明n≥2时超平面的个数不能减少,且坐标平面不能推广至一般超平面。

Based on the derived holomorphic curves,the Milloux type inequality of holomorphic curves is established,and the Picard type theorem is proved:let f be a holomorphic curve from C to P^(n)(C),f is a derived holomorphic curve of f and{H_j}^(2n+1)_(j=1)be hyperplanes in P^(n)(C)located in general position,if f omits the hyperplane family{H_j}^(n+1)_(j=1),f omits the hyperplane family{H_j}(2n+1)j=n+2,then f is constant,where H_(1),H_(2),…,H_(n+1)are n+1coordinate hyperplanes.And some examples are given to show that the number of hyperplanes cannot be reduced and the coordinate hyperplanes cannot be generalized to arbitrary hyperplanes when n≥2.