ENRIQUES’ CLASSIFICATION IN CHARACTERISTIC $p>0$ : THE $P_{12}$ -THEOREM
ENRIQUES’ CLASSIFICATION IN CHARACTERISTIC $p>0$ : THE $P_{12}$ -THEOREM
复制标题
恩里克斯的 $p>0$ 特征分类：$P_{12}$ -定理
DOI：
10.1017/nmj.2018.8
复制
发表时间：
2017
影响因子：
0.8
通讯作者：
Binru Li
中科院分区：
文献类型：
--
作者：
F. Catanese;Binru Li
本文的主要目标是证明 Castelnuovo–Enriques 的 $P_{12}$ - 定理（代数曲面的粗略分类的精确版本）也适用于在正特征代数闭域 $k$ 上定义的代数曲面 $S$ ( $\text{char}(k)=p>0$ ）。该结果依赖于描述适当椭圆或适当准椭圆表面（小平维数等于 1 的表面）的多质生长的主要定理。我们还讨论了极限情况，即表明主定理的结果是尖锐的曲面族。
The main goal of this paper is to show that Castelnuovo–Enriques’ $P_{12}$ - theorem (a precise version of the rough classification of algebraic surfaces) also holds for algebraic surfaces $S$ defined over an algebraically closed field $k$ of positive characteristic ( $\text{char}(k)=p>0$ ). The result relies on a main theorem describing the growth of the plurigenera for properly elliptic or properly quasielliptic surfaces (surfaces with Kodaira dimension equal to 1). We also discuss the limit cases, i.e., the families of surfaces which show that the result of the main theorem is sharp.