论文标题
分解统计和错误的配置空间
Factorization statistics and bug-eyed configuration spaces
论文作者
论文摘要
Hyde的最新定理证明，在有限字段上随机多项式的因素化统计数据受对称群体在$ \ Mathbb r^3 $中的$ n $不同有序积分的配置空间中的作用。海德问是否可以通过几何解释这个结果。我们给出了Hyde定理的几何证明，作为Grothendieck的实例-Lefschetz Trace公式应用于有趣的，高度分离的代数空间。我们方法的一个优点是它统一地概括为任意的Weyl群。在此过程中，我们研究了某些非Hausdorff模型，以提供超平面布置的补充，这是Proudfoot首先引入的。
A recent theorem of Hyde proves that the factorizations statistics of a random polynomial over a finite field are governed by the action of the symmetric group on the configuration space of $n$ distinct ordered points in $\mathbb R^3$. Hyde asked whether this result could be explained geometrically. We give a geometric proof of Hyde's theorem as an instance of the Grothendieck--Lefschetz trace formula applied to an interesting, highly nonseparated algebraic space. An advantage of our method is that it generalizes uniformly to an arbitrary Weyl group. In the process we study certain non-Hausdorff models for complements of hyperplane arrangements, first introduced by Proudfoot.
