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

Abstract

This paper is based on the paper [1], where two classification theorems for locally free sheaves on supermanifolds were proved and a spectral sequence for a locally free sheaf of modules $\varepsilon$ was obtained. We consider another filtration of the locally free sheaf $\varepsilon$, the correspondingc lassification theorem and the spectral sequence, which is more convenient in some cases. The methods, which we are usinghe re, are similar to [1, 2].

The first spectral sequence of this kind was constructed by A.L. Onishchik in [2] for the tangent sheaf of a supermanifold. However, the spectral sequence considered in this paper is not a generalization of Onishchik’s spectral sequence from [2].

Mathematics Subject Classification (2010). Primary 32C11; Secondary 58A50.