论文标题
在特征$> 3 $的三维日志规范丰度上注意
Note on the 3-dimensional log canonical abundance in characteristic $>3$
论文作者
论文摘要
在本文中，我们证明了对原木三倍对的非趋势和一些特殊情况，比代数封闭的特征性特征$ p> 3 $的代数封闭的场$ k $。更确切地说，我们证明，如果$（x，b）$是$ k $上的投影登录规范三倍对，而$ k_ {x}+b $是伪有效的，则$κ（k_ {x}+b）\ geq 0 $ $ k_ {x}+b $是半ample。 作为应用程序，我们表明，有限地生成了投影型原木规范三倍对的日志典范三倍对，并且当nef dimension $ n（k_ {x}+b）\ leq 2 $或Albanese $ a_ __ {x}：x \ to x \ to \ to \ mathrm {alb iS x）（x）（x）（x）此外，我们证明KLT三倍对$ k $的丰度意味着对$ k $的原木规范三倍对的丰度。
In this paper, we prove the non-vanishing and some special cases of the abundance for log canonical threefold pairs over an algebraically closed field $k$ of characteristic $p > 3$. More precisely, we prove that if $(X,B)$ be a projective log canonical threefold pair over $k$ and $K_{X}+B$ is pseudo-effective, then $κ(K_{X}+B)\geq 0$, and if $K_{X}+B$ is nef and $κ(K_{X}+B)\geq 1$, then $K_{X}+B$ is semi-ample. As applications, we show that the log canonical rings of projective log canonical threefold pairs over $k$ are finitely generated and the abundance holds when the nef dimension $n(K_{X}+B)\leq 2$ or when the Albanese map $a_{X}:X\to \mathrm{Alb}(X)$ is non-trivial. Moreover, we prove that the abundance for klt threefold pairs over $k$ implies the abundance for log canonical threefold pairs over $k$.
