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arXiv · 1904.11409

Configurations of noncollinear points in the projective plane

Ronno Das·Ben O'Connor
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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 $H^*(F_n; \mathbb{Q})$ as an $S_n$-representation. The cases $n = 5, 6$ are computed via the Grothendieck--Lefschetz trace formula in \'etale cohomology and certain "twisted" point counts for analogous spaces over $\mathbb{F}_q$.

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Ronno Das, Ben O'Connor. 2019-04-25. Configurations of noncollinear points in the projective plane. https://doi.org/10.2140/agt.2021.21.1941

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