On some minimal supervarieties of exponential growth

In the paper we investigate minimal supervarieties of given superexponent over fields of characteristic zero. We show that any minimal supervariety of finite basic rank is generated by one of the minimal superalgebras, introduced by Giambruno and Zaicev in 2003. Furthermore it is proved that any minimal superalgebra, whose graded simple components of the semisimple part are simple, generates a minimal supervariety. Finally we state that the same conclusion holds when the semisimple part of a minimal superalgebra has exactly two arbitrary graded simple components.