标题： 坎帕纳关于数值等价除子的orbifold猜想 显示英文标题

标题： Campana's orbifold conjecture for numerically equivalent divisors

摘要： 我们证明了如下版本的坎帕纳叠 orbifold 猜想：设$X$为一维数为$n$的复光滑射影簇。设$D_1,\ldots,D_{n+1}$为$\mathbb Z$-线性无关的有效除子，位于${\rm Div}(X)$中，且$D:=D_1+\cdots+D_{n+1}$为$X$的正规横截除子。进一步假设它们数值上是平行的。 设 $\Delta=\sum_{i=1}^{n+1} (1-m_i^{-1}) D_i$ 且设 $f:\mathbb C\to (X,\Delta) $ 为一个轨道整体曲线。 那么，存在正整数$\ell$，使得orbifold$ (X,\Delta_{\ell}) $是一般型的，其中 $\Delta_{\ell}=\sum_{i=1}^{n+1} (1-\frac1{\ell})D_i$，并且如果$f$在$D_i$和$1\le i\le n+1$上至少具有多重度$\ell$，则$f$必须是代数退化的。 显示英文摘要

摘要： We prove the following version of the Campana's orbifold conjecture: Let $X$ be a complex non-singular projective variety of dimension $n$. Let $D_1,\ldots,D_{n+1}$ be $\mathbb Z$-linearly independent effective divisors in ${\rm Div}(X)$ and $D:=D_1+\cdots+D_{n+1}$ be a normal crossing divisor of $X$. Assume furthermore that they are numerically parallel. Let $\Delta=\sum_{i=1}^{n+1} (1-m_i^{-1}) D_i$ and let $f:\mathbb C\to (X,\Delta) $ be an orbifold entire curve. Then, there exists a positive integer $\ell$ such that, the orbifold $ (X,\Delta_{\ell}) $ is of general type, where $\Delta_{\ell}=\sum_{i=1}^{n+1} (1-\frac1{\ell})D_i$, and if $f$ has multiplicity at least $\ell$ along $D_i$, $1\le i\le n+1$, then $f$ must be algebraically degenerate.