论文标题
超平面布置的投影尺寸
Projective dimensions of hyperplane arrangements
论文作者
论文摘要
我们为超平面布置的对数推导模块的投射维度建立了一般理论。其中包括添加删除和限制定理，Yoshinaga型结果以及超平面布置的射影尺寸的划分定理。它们是自由安排案例的概括，当投影维度为零时，可以将其视为我们结果的特殊情况。证明它们的关键是确定欧拉和齐格勒限制图的溢流性的几种新方法，当射影维度并非所有本地化最大时，这都是组合的。此外，我们介绍了一类新的安排，其中投影维度是合理确定的。
We establish a general theory for projective dimensions of the logarithmic derivation modules of hyperplane arrangements. That includes the addition-deletion and restriction theorem, Yoshinaga-type result, and the division theorem for projective dimensions of hyperplane arrangements. They are generalizations of the free arrangement cases, that can be regarded as the special case of our result when the projective dimension is zero. The keys to prove them are several new methods to determine the surjectivity of the Euler and the Ziegler restriction maps, that is combinatorial when the projective dimension is not maximal for all localizations. Also, we introduce a new class of arrangements in which the projective dimension is comibinatorially determined.
