Even-homogeneous supermanifolds on the complex projective line

TL;DR

This paper classifies even-homogeneous complex supermanifolds of dimension 1|m on the complex projective line, providing explicit descriptions for each case up to isomorphism.

Contribution

It offers a complete classification and explicit local descriptions of even-homogeneous supermanifolds on CP^1 for dimensions 1|m with m ≤ 3.

Findings

Classification of supermanifolds up to isomorphism

Explicit local chart descriptions

Complete list for dimensions 1|m, m ≤ 3

Abstract

The classification of even-homogeneous complex supermanifolds of dimension 1|m, m\leq 3, on CP^1 up to isomorphism is given. An explicit description of such supermanifolds in terms of local charts and coordinates is obtained.