A birational Nevanlinna constant and its consequences
A birational Nevanlinna constant and its consequences
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DOI：
10.1353/ajm.2020.0022
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发表时间：
2016-08
影响因子：
1.7
通讯作者：
M. Ru;Paul Vojta
中科院分区：
文献类型：
--
作者：
M. Ru;Paul Vojta
本文的目的是修正第一作者关于射影变化$X$上有效Cartier除数的Nevanlinna常数${\rm Nev}(D)$的概念。修改后的概念称为{\ \ birational Nevanlinna常数}，用${\rm Nev}_{\rm bir}}(D)$表示。${\rm Nev}(D)$和${\rm Nev}_{{\rm bir}}(D)$的目标是使用Faltings和W\ {u}stholz引入的过滤方法来测量什么是可能的，Corvaja和Zannier进一步发展了过滤方法，Evertse和Ferretti独立地发展了过滤方法。利用Autissier的后续工作，通过计算${\rm Nev}_{{\rm bir}}(D)$，我们建立了一个算术和复数情况下的一般结果（见第1节中的一般定理），将everts - ferretti和Ru的结果推广到一般除数。${\rm Nev}_{{\rm bir}}(D)$这个概念最初来自涉及Weil函数的应用，但它也可以通过适当的birational映射提升Cartier除数的局部有效性来定义。
abstract:The purpose of this paper is to modify the notion of the Nevanlinna constant ${\rm Nev}(D)$ introduced by the first author for an effective Cartier divisor on a projective variety $X$. The modified notion is called the {\it birational Nevanlinna constant} and is denoted by ${\rm Nev}_{{\rm bir}}(D)$. The goal of ${\rm Nev}(D)$ and ${\rm Nev}_{{\rm bir}}(D)$ is to measure what is possible using the filtration method introduced by Faltings and W\"{u}stholz, and further developed by Corvaja and Zannier and, independently, by Evertse and Ferretti. By computing ${\rm Nev}_{{\rm bir}}(D)$ using subsequent work of Autissier, we establish a general result (see the General Theorem in Section 1), in both the arithmetic and complex cases, which extends the results of Evertse-Ferretti and of Ru to general divisors. The notion ${\rm Nev}_{{\rm bir}}(D)$ originally came from applications involving Weil functions, but it also can be defined in terms of local effectivity of Cartier divisors after lifting by a proper birational map.