Graded cocharacters of minimal subvarieties of supervarieties of almost polynomial growth

The sequence of graded codimensions of a minimal supervariety of polynomial growth grows like n(t), but any proper subvariety grows like n(s) with s < t. Such supervarieties are the building blocks of general supervarieties of polynomial growth. In this paper, we exhibit the decompositions of the graded cocharacters of all minimal subvarieties of supervarieties of almost polynomial growth and compute their graded colengths. Furthermore, for a finite dimensional superalgebra A such that its sequence of graded codimensions grows like nt we exhibit an upper bound for the nth graded colength of A which depends only on t and on two parameters related to A such as its dimension and the index of nilpotence of its Jacobson radical J (A). (C) 2014 Elsevier B.V. All rights reserved.