The Hesse pencil of plane cubic curves by Michela Artebani and Igor Dolgachev (2009)

Primary author-hosted manuscript: sites.lsa.umich.edu/idolga-new/wp-content/uploads/sites/1467/2024/08/hesse09.pdf

Publisher: ems.press/journals/lem/articles/12146

Preprint: arxiv.org/abs/math/0611590

Section 2, manuscript pp.3–5: Hesse equations, common flex/base points, normal form and Hessians. Published in L’Enseignement Mathématique 55 (2009), pp.235–273. The wiki calculations explicitly use complex coefficients to avoid small-characteristic Hessian degeneracies.