论文标题
超平面布置及其曲线复合物的收益
Bordifications of hyperplane arrangements and their curve complexes
论文作者
论文摘要
$ \ Mathbb c^n $中的超平面布置的补充具有自然的歧化，即通过去除（或“或“炸毁”）超平面及其某些交叉点形成的角落。当安排是真正的简单布置的络合时，界化与哈维的模量空间的界面非常相似。我们证明，界面的通用覆盖物的面是由简单复合物$ \ Mathcal {C} $的简单进行了参数，其顶点是该布置补充基本基本组的不可还原的“抛物线亚组”。因此，复杂的$ \ MATHCAL {C} $在安排补充方面扮演着与曲线复合体对模量空间所扮演的类似角色。同样，与曲线复合物和球形建筑物类似，我们证明$ \ MATHCAL {C} $具有楔形球体的同型类型。
The complement of an arrangement of hyperplanes in $\mathbb C^n$ has a natural bordification to a manifold with corners formed by removing (or "blowing up") tubular neighborhoods of the hyperplanes and certain of their intersections. When the arrangement is the complexification of a real simplicial arrangement, the bordification closely resembles Harvey's bordification of moduli space. We prove that the faces of the universal cover of the bordification are parameterized by the simplices of a simplicial complex $\mathcal{C}$, the vertices of which are the irreducible "parabolic subgroups" of the fundamental group of the arrangement complement. So, the complex $\mathcal{C}$ plays a similar role for an arrangement complement as the curve complex does for moduli space. Also, in analogy with curve complexes and with spherical buildings, we prove that $\mathcal{C}$ has the homotopy type of a wedge of spheres.
