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Библиогр.: 39 назв.

We define a super analog of the classical Plucker embedding of the Grassmannian into a projective space. One of the difficulties of the problem is rooted in the fact that super exterior powers Lambda(r vertical bar s) (V) are not a simple generalization from the completely even case (this works only for r vertical bar 0 when it is possible to use Lambda(r)(V)). To construct the embedding we need to non-trivially combine a super vector space V and its parity-reversion Pi V. Our super Plucker map takes the Grassmann supermanifold G(r vertical bar s)(V) to a weighted projective space P-1,P--1 (Lambda(r vertical bar s)(V) circle plus Lambda(s vertical bar r)(Pi V)) with weights +1, -1. A simpler map G(r vertical bar 0)(V) -> P(Lambda(r)(V)) works for the case s = 0. We construct a super analog of Plucker coordinates, prove that our map is an embedding, and obtain super Plucker relations. We analyze another type of relations (due to Khudaverdian) and show their equivalence with the super Plucker relations for r vertical bar s = 2 vertical bar 0. We discuss application to much sought-after super cluster algebras and construct a super cluster structure for G(2)(R-4 vertical bar 1) and G(2)(R-5(vertical bar 1)).