论文标题
低维度的非通用安排
Non-very generic arrangements in low dimension
论文作者
论文摘要
The discriminantal arrangement $\mathcal{B}(n,k,\mathcal{A})$ has been introduced by Manin and Schectman in 1989 and it consists of all non-generic translates of a generic arrangement $\mathcal{A}$ of n hyperplanes in a $k$-dimensional space.众所周知，它的组合依赖于原始布置A，如果拜耳和布兰特[3]之后，如果诱导的判别安排的相交晶格具有最大的基数，则称为非常通用的A，而非非常通用。虽然$ \ Mathcal {b}的组合学的完整描述（n，k，k，\ mathcal {a}）$当$ \ mathcal {a} $是非常通用的（请参阅[2]）时，在非广告中，很少有人知道。即使提供了非非常通用安排的例子，也被证明是一项非平凡的任务（见[17]）。在本文中，我们表征，分类并提供了低维度的非广泛安排的示例。
The discriminantal arrangement $\mathcal{B}(n,k,\mathcal{A})$ has been introduced by Manin and Schectman in 1989 and it consists of all non-generic translates of a generic arrangement $\mathcal{A}$ of n hyperplanes in a $k$-dimensional space. It is known that its combinatorics depends on the original arrangement A which, following Bayer and Brandt [3], is called very generic if the intersection lattice of the induced discriminantal arrangement has maximum cardinality, non-very generic otherwise. While a complete description of the combinatorics of $\mathcal{B}(n,k,\mathcal{A})$ when $\mathcal{A}$ is very generic is known (see [2]), very few is known in the non-very generic case. Even to provide examples of non very generic arrangements proved to be a non-trivial task (see [17]). In this paper, we characterize, classify and provide examples of non-very generic arrangements in low dimension.
