Non-Projected Supermanifolds and Embeddings in Super Grassmannians

Abstract

In this paper we give a brief account of the relations between non-projected supermanifolds and projectivity in supergeometry. Following the general results (L. Sergio et al., 2018), we study an explicit example of non-projected and non-projective supermanifold over the projective plane and show how to embed it into a super Grassmannian. The geometry of super Grassmannians is also reviewed in detail.

Keywords

• supermanifold
• Grassmannian algebra
• superspace