Embeddings of Complex Supermanifolds

TL;DR

This paper investigates the conditions under which submanifolds of split complex supermanifolds are themselves split, with specific applications to superspace embeddings over rational normal curves.

Contribution

It provides new criteria for when submanifolds of split supermanifolds are split, focusing on embeddings over rational normal curves.

Findings

Criteria established for submanifold splitting

Application to superspace embeddings over rational normal curves

Insights into the structure of complex supermanifolds

Abstract

In this article we present a study of embeddings of complex supermanifolds. We are broadly guided by the question: when will a submanifold of a split supermanifold itself be split? As an application of our study, we will address this question for certain superspace embeddings over rational normal curves.