Hexagonal pencils of cubic plane curves

Joel Langer; Jeremy Wall

doi:10.4171/lem/1062

JournalslemVol. 70, No. 3/4pp. 479–497

Hexagonal pencils of cubic plane curves

Joel Langer
Case Western Reserve University, Cleveland, USA
Jeremy Wall
Case Western Reserve University, Cleveland, USA

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Abstract

This expository paper considers real cubic plane curves as combinations $C = a_{1} T_{1} + a_{2} T_{2}$ of two real triangles meeting in nine distinct points. Our study of hexagonal pencils, defined by $C$ with parameters $a_{i} \in R$ , picks up on some themes of a recent paper on cubics by Bonifant and Milnor (2017).

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Joel Langer, Jeremy Wall, Hexagonal pencils of cubic plane curves. Enseign. Math. 70 (2024), no. 3/4, pp. 479–497

DOI 10.4171/LEM/1062