On the structure of 4-folds with a hyperplane section which is a P 1 bundle over a surface that fibres over a curve
On the structure of 4-folds with a hyperplane section which is a P 1 bundle over a surface that fibres over a curve
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具有超平面截面的 4 折结构，该超平面截面是曲面上的 P 1 束，纤维在曲线上
DOI：
10.1017/s0027763000002622
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发表时间：
1987
影响因子：
0.8
通讯作者：
A. Sommese
中科院分区：
文献类型：
--
作者：
M. Fania;E. Sato;A. Sommese
在本文中，我们想分析一个四维射影簇X的结构，它有一个光滑的样本因子a，即光滑表面S上的P1束π: a→S。在[Fa+So]中，作为一个更一般的结果的结果，第一和第三作者确定了P1束a的底S有h2,0()≠0的覆盖时X的结构。这里我们看看除了那些曲面是稳定的二阶向量束在曲线上的投影之外的其他情况（结果显然对S有理是正确的）。
In this article we want to analyze the structure of a 4 dimensional projective variety X which has a smooth ample divisor A that is a P1 bundle π : A→S over a smooth surface S. In [Fa+So], as a consequence of a more general result, the first and third authors determined the structure of X in the case the base S of the P1 bundle A has a cover with h2,0()≠0. Here we look at the remaining cases except for those surfaces which are the projectivization of a stable rank two vector bundle over a curve (the result is obviously true for S rational).