On a general Diophantine inequality

Abstract

In [Ru15], the author introduced the notion of Nevanlinna constant (denoted by $Nev(D)$) for any effective Cartier divisor $D$ on a normal projective variety $X$, and established a defect relation for Zariski-dense holomorphic mappings $f: {\mathbb C}\rightarrow X$ in terms of $Nev(D)$. In this paper, we prove its counterpart result in Diophantine approximation, according to Vojta's correspondence (or Vojta's dictionary [Voj87]). The results obtained gave the quantitative extension of the earlier results of Corvaja-Zannier [CZ04a,CZ04b], Evertse-Ferretti [EF02, EF08], A. Levin [Lev09], P. Autissier [Aut1], and others.