Non-Projected Supermanifolds and Embeddings in Super Grassmannians

TL;DR

This paper explores the relationship between non-projected supermanifolds and projectivity, providing an explicit example of embedding a non-projective supermanifold into a super Grassmannian, and reviewing super Grassmannian geometry.

Contribution

It presents an explicit example of a non-projected, non-projective supermanifold embedded into a super Grassmannian, expanding understanding of supergeometry embeddings.

Findings

Explicit example of non-projected supermanifold over the projective plane.

Demonstration of embedding into super Grassmannian.

Detailed review of super Grassmannian geometry.

Abstract

In this paper we give a brief account of the relations between non-projected supermanifolds and projectivity in supergeometry. Following the general results of arXiv:1706.01354, we study an explicit example of non-projected and non-projective supermanifold over the projective plane and we show how to embed it into a super Grassmannian. The geometry of super Grassmannians is also reviewed in details.