The Hesse pencil of plane cubic curves

  • Michela Artebani

    Universidad de Concepción, Chile
  • Igor V. Dolgachev

    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 surfaces with Picard number 20 which arise naturally in connection with this configuration.

Cite this article

Michela Artebani, Igor V. Dolgachev, The Hesse pencil of plane cubic curves. Enseign. Math. 55 (2009), no. 3/4, pp. 235–273

DOI 10.4171/LEM/55-3-3