Seshadri-exceptional foliations
Seshadri-exceptional foliations
复制标题
Seshadri-特殊的叶状结构
DOI：
10.1007/s00208-002-0377-6
复制
发表时间：
2003
影响因子：
1.4
通讯作者：
J. Keum
中科院分区：
文献类型：
--
作者：
Jun;J. Keum
摘要：光滑射影簇X上的一个样本线丛L的最大Seshadri数μ（L）度量了线丛L在X的一般点处的局部正性。 通过改进Ein-Kück-Lazarsfeld方法，得到了一类簇的μ（L）关于Ln，n=dim（X）的下界.其主要思想是表明，如果某个下界是违反的，存在一个非平凡的叶理的品种，其叶片覆盖的特殊曲线。在许多例子中，可以证明这样的叶理一定是平凡的，并得到μ（L）的下界。例子包括Picard数为1的光滑曲面上的超平面线丛和Picard数为1的光滑三重曲面上的样本线丛。
Abstract. The maximal Seshadri number μ(L) of an ample line bundle L on a smooth projective variety X measures the local positivity of the line bundle L at a general point of X. By refining the method of Ein-Küchle-Lazarsfeld, lower bounds on μ(L) are obtained in terms of Ln, n=dim(X), for a class of varieties. The main idea is to show that if a certain lower bound is violated, there exists a non-trivial foliation on the variety whose leaves are covered by special curves. In a number of examples, one can show that such foliations must be trivial and obtain lower bounds for μ(L). The examples include the hyperplane line bundle on a smooth surface in ℙ3 and ample line bundles on smooth threefolds of Picard number 1.