Degenerations of Jordan superalgebras (Q2272691)

The authors describe degenerations of three-dimensional Jordan superalgebras over the complex field. In particular, all irreducible components in the corresponding varieties are described. Since there is essentially only one Jordan superalgebra of type \((0,3)\) in the above mentioned class, and the ones of type \((3,0)\) have been described in a previous work (reference [\textit{I. Gorshkov} et al., ``Degenerations of Jordan algebras'', Preprint, \url{arXiv:1707.08836}] in the paper), the authors focus on type \((1,2)\) and \((2,1)\). For type \((1,2)\) the classification of three-dimensional Jordan superalgebras by \textit{M. E. Martin} [``Classification of three-dimensional Jordan superalgebras'', Preprint, \url{arXiv:1708.01963}] is used. This classification contains 11 cases and then the primary degeneracy graph as well as the the primary nondegeneracy data is explained. Also the irreducible components of the variety of Jordan superalgebras of type \((1,2)\) are described giving that there are 7 rigid algebras. Finally a parallel program for Jordan superalgebras of type \((2,1)\) is also accomplished.