论文标题
对数透明术图的界面图，以纪录总型表面为正特征
Boundedness of log-pluricanonical maps for surfaces of log-general types in positive characteristic
论文作者
论文摘要
在本文中，我们证明了以下有限的结果：修复DCC集$ i \ subset [0，1] $。令$ \ mathfrak {d} $是满足以下属性的所有日志对$（x，δ）$的集合：（i）$ x $是在代数封闭的字段上定义的投影表面，（ii）$（x，δ）$是log canonical canonical canonical canonical and canonical and caneficiatients us $δ$ in $ i $ $ i $，yii $ i $ i IS $ iii $ iii $ iii）$ k_xx $ k_xx+xxx++然后有一个正整数$ n = n（i）$仅取决于集合$ i $，以使线性系统$ | \ lceil m（k_x+δ）\ rceil | $ | $ | $ | $将其图像定义为所有$ m \ geq n $ and $ geq n $和$（x，x，x，x，x，x，d} $
In this article we prove the following boundedness result: Fix a DCC set $I\subset [0, 1]$. Let $\mathfrak{D}$ be the set of all log pairs $(X, Δ)$ satisfying the following properties: (i) $X$ is a projective surface defined over an algebraically closed field, (ii) $(X, Δ)$ is log canonical and the coefficients of $Δ$ are in $I$, and (iii) $K_X+Δ$ is big. Then there is a positive integer $N=N(I)$ depending only on the set $I$ such that the linear system $|\lceil m(K_X+Δ)\rceil|$ defines a birational map onto its image for all $m\geq N$ and $(X, Δ)\in\mathfrak{D}$
