2020/04/30 by Dan Petersen, Philip Tosteson · 2 citations
Mathematics · #Action (physics) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic number #Combinatorics #Discrete mathematics #Factorization #Field (mathematics) #Finite field #Group (periodic table) #Hyperplane #Mathematical analysis #Mathematics #Polynomial #Pure mathematics #Space (punctuation) #TRACE (psycholinguistics) #math.AG #math.AT #math.CO #math.NT #math.RT
paper · pdf · doi:10.2140/gt.2021.25.3691
published in Geometry & Topology 25(7), 3691-3723 (Mathematical Sciences Publishers) · 19 pages. v2: added reference to prior work of Proudfoot v3: final version to appear in G&T
arxiv created 2021/10/03 · openalex publication_date 2021/12/31 · arxiv updated 2022/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 R3. 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.