论文标题
$ \ Mathbb p^2 $和Alexander Duality的网
Nets in $\mathbb P^2$ and Alexander Duality
论文作者
论文摘要
$ \ Mathbb {p}^2 $中的net是行$ \ mathcal a $的配置，点$ x $满足某些发病率的属性。网中出现在各种环境中，从准元素到组合设计到Kac-Moody代数的分类到共同平面布置的共同基因座。对于Matroid $ m $和等级$ r $，我们将单一理想（Orlik-Solomon Ideal的单一变体）与$ M $等级$ \ le R $的公寓相关联。在$ \ mathbb {p}^2 $中的行安排的背景下，将亚历山大二元性应用于最终的理想中，可以洞悉网络的组合结构。
A net in $\mathbb{P}^2$ is a configuration of lines $\mathcal A$ and points $X$ satisfying certain incidence properties. Nets appear in a variety of settings, ranging from quasigroups to combinatorial design to classification of Kac-Moody algebras to cohomology jump loci of hyperplane arrangements. For a matroid $M$ and rank $r$, we associate a monomial ideal (a monomial variant of the Orlik-Solomon ideal) to the set of flats of $M$ of rank $\le r$. In the context of line arrangements in $\mathbb{P}^2$, applying Alexander duality to the resulting ideal yields insight into the combinatorial structure of nets.
