A Classification Theorem and a Spectral Sequence for a Locally Free Sheaf Cohomology of a Supermanifold

This paper is based on the paper (1), where two classification the- orems for locally free sheaves on supermanifolds were proved and a spectral sequence for a locally free sheaf of modules ℰ was obtained. We consider another filtration of the locally free sheaf ℰ , the correspondingclassification theorem and the spectral sequence, which is more convenient in some cases. The methods, which we are usinghere, are similar to (1, 2). The first spectral sequence of this kind was constructed by A.L. Oni- shchik in (2) for the tangent sheaf of a supermanifold. However, the spectral sequence considered in this paper is not a generalization of Onishchik's spec- tral sequence from (2). Mathematics Subject Classification (2010). Primary 32C11; Secondary 58A50.