论文标题
退化第二个主要定理和施密特的子空间定理的概括
Generalizations of degeneracy second main theorem and Schmidt's subspace theorem
论文作者
论文摘要
在本文中，通过介绍有关投射品种的Hypersurfaces家族的“ \ textit {分布式常数}”的概念，我们证明了Nevanlinna理论中的第二个主要定理，用于具有斑射性品种中的Hypersurface的任意家族。我们的第二个主要定理概括并改善了与超曲面的Meromorphic映射的先前结果，特别是对于代数归化映射以及亚属性位置的Hypersurfaces家族。同类似曲线的类似结果，从复杂的光盘到项目变化，以及用于完整的Kähler歧管上的Meromormormormormorphic映射的有限生长指数的结果。为了最后一个目标，我们将证明施密特的统一多项式家庭的子空间定理，这是我们第二个主要定理的数字理论中的对应物。我们的这些结果是所有先前结果的概括和改进。
In this paper, by introducing the notion of "\textit{distributive constant}" of a family of hypersurfaces with respect to a projective variety, we prove a second main theorem in Nevanlinna theory for meromorphic mappings with arbitrary families of hypersurfaces in projective varieties. Our second main theorem generalizes and improves previous results for meromorphic mappings with hypersurfaces, in particular for algebraically degenerate mappings and for the families of hypersurfaces in subgeneral position. The analogous results for the holomorphic curves with finite growth index from a complex disc into a project variety, and for meromorphic mappings on a complete Kähler manifold are also given. For the last aim, we will prove a Schmidt's subspace theorem for an arbitrary families of homogeneous polynomials, which is the counterpart in Number theory of our second main theorem. Our these results are generalizations and improvements of all previous results.
