Configurations of noncollinear points in the projective plane

Abstract

We consider the space $F_n$ of configurations of $n$ points in $P^2$ satisfying the condition that no three of the points lie on a line. For $n=4,5,6$, we compute $H^{\ast }(F_n;\mathbb{Q})$ as an $S_n$-representation. The cases $n=5,6$ are computed via the Grothendieck--Lefschetz trace formula in étale cohomology and certain "twisted" point counts for analogous spaces over ${\mathbb{F}}_q$.

26 pages, 14 figures

References in corpus (3)

• A spectral sequence for stratified spaces and configuration spaces of points
• Counting Arcs in Projective Planes via Glynn's Algorithm
• Equivariant Cohomology of the Moduli Space of Genus Three Curves with Symplectic Level Two Structure via Point Counts