Configurations of noncollinear points in the projective plane

Das, Ronno; O’Connor, Ben

doi:10.2140/agt.2021.21.1941

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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

DOI: 10.2140/agt.2021.21.1941

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 $H^{*} (F_{n}; ℚ)$ 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 $𝔽_{q}$ .

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

Volume 21, issue 4 (2021)