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A recent theorem of Hyde proves that the factorization statistics of a random polynomial over a finite field are governed by the action of the symmetric group on the configuration space of distinct ordered points in . 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 any Weyl group. In the process we study certain non-Hausdorff models for complements of hyperplane arrangements, first introduced by Proudfoot.
Petersen, Dan 1 ; Tosteson, Philip 2
@article{GT_2021_25_7_a7, author = {Petersen, Dan and Tosteson, Philip}, title = {Factorization statistics and bug-eyed configuration spaces}, journal = {Geometry & topology}, pages = {3691--3723}, publisher = {mathdoc}, volume = {25}, number = {7}, year = {2021}, doi = {10.2140/gt.2021.25.3691}, url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2021.25.3691/} }
TY - JOUR AU - Petersen, Dan AU - Tosteson, Philip TI - Factorization statistics and bug-eyed configuration spaces JO - Geometry & topology PY - 2021 SP - 3691 EP - 3723 VL - 25 IS - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/gt.2021.25.3691/ DO - 10.2140/gt.2021.25.3691 ID - GT_2021_25_7_a7 ER -
Petersen, Dan; Tosteson, Philip. Factorization statistics and bug-eyed configuration spaces. Geometry & topology, Tome 25 (2021) no. 7, pp. 3691-3723. doi : 10.2140/gt.2021.25.3691. http://geodesic.mathdoc.fr/articles/10.2140/gt.2021.25.3691/
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