Free pencils on divisors
Free pencils on divisors
复制标题
除数上的免费铅笔
DOI：
10.1007/bf01460982
复制
发表时间：
1993
影响因子：
1.4
通讯作者：
R. Paoletti
中科院分区：
文献类型：
--
作者：
R. Paoletti
设X是定义在代数闭域上的光滑射影簇，X中的Y是X中既约又不可约的充足因子。本文给出了基点自由束成为基点自由束在上的限制的一个数值充分条件，并将这一结果推广到自由束族和任意光滑曲线的态射。塞拉诺已经研究了这个问题的情况下，n=2和3，和里德然后攻击它的caseusing矢量束方法的基础上博戈莫洛夫的不稳定定理的表面（char（k）=0）。这里给出的论点是基于博戈莫洛夫定理的n维品种，并在其最近的适应设置的总理charachterstic（由于谢泼德巴伦和森胁）。
Let X be a smooth projective variety defined over an algebraically closed field, and let Y in X be a reduced and irreducible ample divisor in X. We give a numerical sufficient condition for a base point free pencil onto be the restriction of a base point free pencil on. This result is then extended to families of pencils and to morphisms to arbitrary smooth curves. Serrano had already studied this problem in the case n=2 and 3, and Reider had then attacked it in the caseusing vector bundle methods based on Bogomolov's instability theorem on a surface (char(k)=0). The argument given here is based on Bogomolov's theorem on an n-dimensional variety, and on its recent adaptations to the setting of prime charachterstic (due to Shepherd-Barron and Moriwaki).