Graded covering of a supermanifold

Abstract

We introduce and investigate the notion of a $\mathbb{Z}$-graded covering for a supermanifold. More precisely, Donagi and Witten suggested a construction of the first obstruction class for splitting of a supermanifold via differential operators. We prove that an infinite prolongation of this construction satisfies some universal properties and can be seen as a covering of a supermanifold in the category of graded manifolds.

The article is a continuation of the unfinished paper arXiv:2103.00665