Geometric classification of nilpotent Jordan algebras of dimension five
  The variety $JorN_{5}$ of five-dimensional nilpotent Jordan algebras structures over an algebraically closed field is investigated. We show that $JorN_{5}$ is the union of five irreducible components, four of them correspond to the Zariski closure of the $GL_5$-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. 
Maria Eugenia Martin, Iryna Kashuba
math.RA