2016/03/12 by Weiyan Chen, Chen, Weiyan · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #math.AG #math.AT #math.CO #math.GT
paper · pdf · doi:10.48550/arxiv.1603.03931
19 pages
arxiv created 2016/03/12 · openalex publication_date 2016/03/12 · arxiv updated 2016/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider two families of algebraic varieties Yn indexed by natural numbers n: the configuration space of unordered n-tuples of distinct points on ℂ, and the space of unordered n-tuples of linearly independent lines in ℂn. Let Wn be any sequence of virtual Sn-representations given by a character polynomial, we compute Hi(Yn; Wn) for all i and all n in terms of double generating functions. One consequence of the computation is a new recurrence phenomenon: the stable twisted Betti numbers limn→∞dim Hi(Yn; Wn) are linearly recurrent in i. Our method is to compute twisted point-counts on the Fq-points of certain algebraic varieties, and then pass through the Grothendieck-Lefschetz fixed point formula to prove results in topology. We also generalize a result of Church-Ellenberg-Farb about the configuration spaces of the affine line to those of a general smooth variety.