论文标题
组合类型的判别安排的分类
A classification of combinatorial types of discriminantal arrangements
论文作者
论文摘要
Manin和Schechtman介绍了一系列的超级平面布置，使经典的编织安排称为$ \ textit {Incriminantal Anchuments} $。 Athanasiadis证明了拜耳和布兰特的猜想，在$ \ textit {非常通用} $安排的情况下，提供了判别安排的完整描述。 Libgober和Settepanella描述了一个足够的几何条件，即在某个安排的依赖性概念方面，给定的布置为$ \ textit {non非常通用} $。 Settepanella和作者概括了引入$ r $ - 集和$ k_ \ mathbb {t} $向量集的依赖关系的概念，并为非非常通用提供了足够的条件，但仍然不方便地通过手动验证。在本文中，我们对$ r $ sem的分类进行分类，并针对非非常通用性提供更明确，更可行的条件。
Manin and Schechtman introduced a family of arrangements of hyperplanes generalizing classical braid arrangements, which they called the $\textit{discriminantal arrangements}$. Athanasiadis proved a conjecture by Bayer and Brandt providing a full description of the combinatorics of discriminantal arrangements in the case of $\textit{very generic}$ arrangements. Libgober and Settepanella described a sufficient geometric condition for given arrangements to be $\textit{non very generic}$ in terms of the notion of dependency for a certain arrangement. Settepanella and the author generalized the notion of dependency introducing $r$-sets and $K_\mathbb{T}$-vector sets, and provided a sufficient condition for non very genericity but still not convenient to verify by hand. In this paper we give a classification of the $r$-sets, and a more explicit and tractable condition for non very genericity.
