论文标题
关于超平面布置的形式和组合形式
On Formality and Combinatorial Formality for hyperplane arrangements
论文作者
论文摘要
如果超平面布置称为形式，则超平面的定义形式之间的所有线性依赖性都是由对应于Condimension二的交叉点的依赖性形式的。这一观念的意义源于以下事实：与非球面补充的复杂布置是正式的。本说明的目的是双重的。尽管Yuzvinsky的作品表明形式不是组合性的，但在我们的第一个主要定理中，我们证明了安排良好性的组合属性确实需要形式。我们的第二个主要定理表明形式是遗传性的，即通过限制。这是相当违反直觉的，相比之下，已知的形式足够的条件，即非球面，烦躁和善良（归功于我们的第一个定理），不是遗传性的。我们还证明，由于勃兰特和terao，$ k $ - 性格的较强财产不是世袭的。
A hyperplane arrangement is called formal provided all linear dependencies among the defining forms of the hyperplanes are generated by ones corresponding to intersections of codimension two. The significance of this notion stems from the fact that complex arrangements with aspherical complements are formal. The aim of this note is twofold. While work of Yuzvinsky shows that formality is not combinatorial, in our first main theorem we prove that the combinatorial property of niceness of arrangements does entail formality. Our second main theorem shows that formality is hereditary, i.e. is passed to restrictions. This is rather counter-intuitive, as in contrast the known sufficient conditions for formality, i.e. asphericity, freeness and niceness (owed to our first theorem), are not hereditary themselves. We also demonstrate that the stronger property of $k$-formality, due to Brandt and Terao, is not hereditary.
