The variety of flexes of plane cubics

Abstract

Let $X$ be the variety of flexes of plane cubics. We prove that (1) $X$ is an irreducible rational algebraic variety endowed with a faithful algebraic action of ${\mathrm{PSL}}_3$; (2) $X$ is ${\mathrm{PSL}}_3$-equivariantly birationally isomorphic to a homogeneous fiber space over ${\mathrm{PSL}}_3/K$ with fiber ${\mathbb{P}}^1$ for some subgroup $K$ isomorphic to the binary tetrahedral group ${\mathrm{SL}}_2({\mathbb{F}}_3)$.

22 pages. Added a remark to statement (H_3) of Lemma 6 (footnote on p. 14). To appear in Proceedings of the Steklov Institute of Mathematics, vol. 329 (2025)

References in corpus (1)

• Rational differential forms on the variety of flexes of plane cubics