被直线覆盖的流形、有缺陷流形及受限的Hartshorne猜想
代数几何
2012-09-11 v3
摘要
由低次方程定义的小余维嵌入流形是Fano流形且被直线覆盖。当通过一般点的直线簇是完备交且具有正确余维时，这些流形恰好是完备交。这使我们能够证明由二次方程定义的流形的Hartshorne猜想，并得到此类Hartshorne流形的列表。利用通过一般点的直线簇的几何性质，我们刻画了对偶有缺陷流形中的卷曲。这导致了对偶缺陷的一个最优界，改进了Ein的结果。我们讨论了我们的猜想：每个具有循环Picard群的对偶有缺陷流形也应是割线有缺陷的，且属于一种非常特殊的类型，即局部二次入口轨迹簇。
引用
@article{arxiv.0909.2763,
title = {Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture},
author = {Paltin Ionescu and Francesco Russo},
journal= {arXiv preprint arXiv:0909.2763},
year = {2012}
}
备注
21 pages; This paper has been withdrawn because its contents were divided into two papers reconstructing integrally this one and resubmitted to arXiv. This was done due to requirements of referee(s)/Editorial Boards