Geometric classification of nilpotent Jordan algebras of dimension five

Abstract

The variety $Jor{N}_5$ of five-dimensional nilpotent Jordan algebras structures over an algebraically closed field is investigated. We show that $Jor{N}_5$ is the union of five irreducible components, four of them correspond to the Zariski closure of the $G{L}_5$-orbits of four rigid algebras and the other one is the Zariski closure of an union of orbits of infinite family of algebras, none of them being rigid.