L’Enseignement Mathématique

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Volume 55, Issue 3/4, 2009, pp. 235–273
DOI: 10.4171/LEM/55-3-3

Published online: 2009-12-31

The Hesse pencil of plane cubic curves

Michela Artebani[1] and Igor V. Dolgachev[2]

(1) Universidad de Concepción, Chile
(2) University of Michigan, Ann Arbor, United States

This is a survey of the classical geometry of the Hesse configuration of 12 lines in the projective plane with relation to the inflection points of a plane cubic curve. We also study two $K3$ surfaces with Picard number 20 which arise naturally in connection with this configuration.

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Artebani Michela, Dolgachev Igor: The Hesse pencil of plane cubic curves. Enseign. Math. 55 (2009), 235-273. doi: 10.4171/LEM/55-3-3