因子分解统计量和有缺陷的配置空间
Factorization statistics and bug-eyed configuration spaces
摘要：
Hyde最近的一个定理证明了有限域上随机多项式的因子分解统计量受对称群在$\mathbb R^3$中$n$不同序点的位形空间上的作用的控制.海德问这个结果是否可以解释几何。我们给出了一个几何证明海德定理的Grothendieck-Lefschetz迹公式应用到一个有趣的，高度非分离的代数空间的一个实例。我们的方法的一个优点是，它一致推广到任意外尔群。在这个过程中，我们研究某些非豪斯多夫模型的补充超平面安排，首先介绍了Proudfoot。
英文摘要：
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.
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