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Configurations of noncollinear points in the projective plane

Ronno Das and Ben O’Connor

Algebraic & Geometric Topology 21 (2021) 1941–1972

We consider the space Fn of configurations of n points in 2 satisfying the condition that no three of the points lie on a line. For n = 4,5,6, we compute H(Fn; ) as an 𝔖n–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 𝔽q.

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collinear, configuration space, cohomology, projective plane, hyperplane complement
Mathematical Subject Classification 2010
Primary: 55R80
Secondary: 14F25, 14J10
Received: 14 January 2020
Revised: 6 August 2020
Accepted: 26 August 2020
Published: 18 August 2021
Ronno Das
Department of Mathematics
University of Chicago
Chicago, IL
United States
Ben O’Connor
Department of Mathematics
University of Chicago
Chicago, IL
United States