Graded Riemann surfaces
type: Item
instance of: scholarly article
title: Graded Riemann surfaces
zbMATH Open document ID: 0659.30038
DOI: 10.1007/BF01225037
author: S. H. Smith
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: What super Riemann surfaces should be is a fundamental question in the theory of superstrings. There has been a lot of activity for describing super Riemann surfaces and the super Teichmüller spaces that classify them. Most descriptions use a subcategory of \(G^{\infty}\)- supermanifolds in which the coordinate charts have a simple form (de Witt manifolds). This paper considers the more restrictive case of Riemann surfaces in the category of graded manifolds. The authors think that the gain in doing this is the evident role of the double cover Sl(2,C) of the Lorentz group in the classification of graded Riemann surfaces. The results are as follows: 1. The group Sl(2,C) plays the role of the Möbius group as the automorphism group of the algebra of graded rational functions. 2. All graded Riemann surfaces occur as quotients of simply connected graded Riemann surfaces by discrete subgroup of Sl(2,C).
Mathematics Subject Classification ID: 30F99
Mathematics Subject Classification ID: 58C50
Mathematics Subject Classification ID: 58A50
zbMATH DE Number: 4077662
zbMATH Keywords: super Riemann surfaces
zbMATH Keywords: superstrings
zbMATH Keywords: graded Riemann surfaces
reviewed by: Yoshihide Kozai
MaRDI profile type: Publication
cites work: Two Approaches to Supermanifolds
cites work: Q3337699
cites work: Super Riemann surfaces: Uniformization and Teichmüller theory
cites work: Q3931656
cites work: A global theory of supermanifolds
Recommended article: Q4488080
Recommended article: Q3709022
Recommended article: Riemann surfaces
Recommended article: Q3003641
Recommended article: Q5458650
Recommended article: Graded Riemann surfaces and Krichever-Novikov algebras
Recommended article: Q3204640
Recommended article: Q5459619
description: scientific article; zbMATH DE number 4077662