论文标题
复杂双曲线歧管的阳性束的阳性
Positivity of the Cotangent Bundle of Complex Hyperbolic Manifolds with Cusps
论文作者
论文摘要
令$ \ overline {x} $为带有边界除数$ d = \ overline {x} \ setMinus x $的cused复数双曲线歧管的环形压实。本文的主要目的是找到$ω^{1} _ {\ overline {x}} $和$ω^{1} _ {\ overline {x}} \ big（big（\ log（d）\ big）$，根据$ x $的$ x $。我们证明，$ω^{1} _ {\ edimine {x}} \ big（\ log（d）\ big）\ langle -r d \ rangle $对于所有足够小的理性数字$ r> 0 $都足够，$ r> 0 $，$ω^{1} _ {1} _ { Modulo $D。$进一步，我们得出的结论是，如果$ x $的cusp均匀深度大于$4π$，那么$ω^{1} _ {\ overline {x}} $就是半emplem us-modulo $ $ $ d $，所有$ x $的$ x $都是$ x $的$ subvariety $ subvariety $ v \ v \ v v \ v \ v \ v \ v \ v \ v \ v \ v \ v v \ $ \ OVILLINE {x} $具有足够的$ k_ {v} $。最后，我们表明，$ \ edline {x} $的最小次数相交的$ x $和$ d $都倾向于在普通覆盖率的塔楼中无限。$ x。
Let $\overline{X}$ be the toroidal compactification of a cusped complex hyperbolic manifold $X=\mathbb{B}^n/Γ$ with the boundary divisor $D=\overline{X}\setminus X$. The main goal of this paper is to find the positivity properties of $Ω^{1}_{\overline{X}}$ and $Ω^{1}_{\overline{X}}\big(\log(D)\big)$ depending intrinsically on $X$. We prove that $Ω^{1}_{\overline{X}}\big(\log(D)\big) \langle -r D \rangle$ is ample for all sufficiently small rational numbers $r >0$, and $Ω^{1}_{\overline{X}}\big(\log(D)\big)$ is ample modulo $D.$ Further, we conclude that if the cusps of $X$ have uniform depth greater than $4π$, then $Ω^{1}_{\overline{X}}$ is semi-ample and is ample modulo $D$, all subvarieties of $X$ are of general type, and every smooth subvariety $V\subset \overline{X}$ intersecting $\overline{X}$ has ample $K_{V}$. Finally, we show that the minimum volume of subvarieties of $\overline{X}$ intersecting both $X$ and $D$ tends to infinity in towers of normal covering of $X.$
