论文标题
封闭式化的概括的第二个主要定理
A generalized second main theorem for closed subschemes
论文作者
论文摘要
令$ y_ {1}，\ ldots，y_ {q} $被关闭的亚chemes，该子机是位于复杂的投影型$ x $ dimensiv $n。$n。$n。$n。$ a $的$ x $ x $的$ \ ell $ -subgeneral位置，让$ a $是$ x. $ x. $ x。 zariski-dense，然后每$ε> 0，$ \ begin {eqnarray*} \ sum^{q} _ { \ left（\ frac {（\ ell-n+κ）（n+1）}κ+ε\ right）t_ {f，a}（r）。 \ end {eqnarray*}由于Heier-Levin [Am J. Math]，这概括了通用位置案例的第二个主要定理。 143（2021），否。 1，213-226]和由于HE-RU引起的亚属性案例[J.数字理论229（2021），125-141]。特别是，只要所有$ y_j $都减少到卡地亚分区，我们还为分布式常数提供了第二个主定理。还给出了相应的Schmidt的子空间定理，用于二芬太汀近似中的封闭式子空间。
Let $Y_{1}, \ldots, Y_{q}$ be closed subschemes which are located in $\ell$-subgeneral position with index $κ$ in a complex projective variety $X$ of dimension $n.$ Let $A$ be an ample Cartier divisor on $X.$ We obtain that if a holomorphic curve $f:\mathbb C \to X$ is Zariski-dense, then for every $ε>0,$ \begin{eqnarray*} \sum^{q}_{j=1}ε_{Y_{j}}(A)m_{f}(r,Y_{j})\leq_{exc} \left(\frac{(\ell-n+κ)(n+1)}κ+ε\right)T_{f,A}(r). \end{eqnarray*}This generalizes the second main theorems for general position case due to Heier-Levin [AM J. Math. 143(2021), no. 1, 213-226] and subgeneral position case due to He-Ru [J. Number Theory 229(2021), 125-141]. In particular, whenever all the $Y_j$ are reduced to Cartier divisors, we also give a second main theorem with the distributive constant. The corresponding Schmidt's subspace theorem for closed subschemes in Diophantine approximation is also given.
