论文标题
非广泛判别安排的线性条件
A linear condition for non-very generic discriminantal arrangements
论文作者
论文摘要
判别安排是在$ k $尺寸空间中$ n $超平面位置的配置的空间（请参阅\ cite {ms}）。与$ k = 1 $的情况不同，它与众所周知的编织布置相对应，在$ k> 1 $的情况下，判别安排具有组合物，取决于原始$ n $ hyperplanes的选择。众所周知，这种组合物在开放式Zariski集合中是恒定的，但要评估或不是$ n $固定的超级平面，属于$ \ Mathcal {z} $被证明是一个非谋取问题。即使简单地提供了不在$ \ Mathcal {z} $中的配置示例仍然是一项艰巨的任务。在本文中，从\ cite {ssc}的最新结果中移动，我们定义了$ \ textIt {弱线性独立性} $条件，如果强加了，如果强加了，允许在$ \ Mathcal {z} $中构建超级平面的配置。我们提供$ 3 $的示例。
The discriminantal arrangement is the space of configurations of $n$ hyperplanes in generic position in a $k$ dimensional space (see \cite{MS}). Differently from the case $k=1$ in which it corresponds to the well known braid arrangement, the discriminantal arrangement in the case $k>1$ has a combinatorics which depends from the choice of the original $n$ hyperplanes. It is known that this combinatorics is constant in an open Zariski set $\mathcal{Z}$, but to assess wether or not $n$ fixed hyperplanes in generic position belongs to $\mathcal{Z}$ proved to be a nontrivial problem. Even to simply provide examples of configurations not in $\mathcal{Z}$ is still a difficult task. In this paper, moving from a recent result in \cite{SSc}, we define a $\textit{weak linear independency}$ condition among sets of vectors which, if imposed, allows to build configurations of hyperplanes not in $\mathcal{Z}$. We provide $3$ examples.
