Degenerations of Jordan Algebras and ''Marginal'' Algebras

We describe all degenerations of the variety ${\mathfrak{J}\mathfrak{o}\mathfrak{r}\mathfrak{d}}_3$ of Jordan algebras of dimension three over $\mathbb{C}\mathrm{.}$ In particular, we describe all irreducible components in ${\mathfrak{J}\mathfrak{o}\mathfrak{r}\mathfrak{d}}_3\mathrm{.}$ For every $n$ we define an $n$-dimensional rigid ‘‘marginal’’ Jordan algebra of level one. Also, we discuss ‘‘marginal’’ algebras in associative, alternative, left alternative, non-commutative Jordan, Leibniz, and anticommutative cases.