Volume 21, issue 4 (2021)

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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
Abstract

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.

Keywords
collinear, configuration space, cohomology, projective plane, hyperplane complement
Mathematical Subject Classification 2010
Primary: 55R80
Secondary: 14F25, 14J10
References
Publication
Received: 14 January 2020
Revised: 6 August 2020
Accepted: 26 August 2020
Published: 18 August 2021
Authors
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