Deformations of complex structures on supermanifolds
type: Item
instance of: scholarly article
title: Deformations of complex structures on supermanifolds
zbMATH Open document ID: 0584.32040
DOI: 10.1007/BF01077827
author: A. Yu. Vajntrob
publication date: 1984-01-01T00:00:00Z
review text: The author defines what is meant by a deformation of a complex supermanifold, defines the analogue of the classical Kodaira-Spencer map, and states the natural generalizations of the Kodaira-Nirenberg-Spencer existence theorems for versal deformations. It is interesting to note that superprojective spaces \(({\mathbb{P}}^{1/4}\), for example) may admit no trivial deformations. This is in line with \textit{P. S. Green}'s example of a non-trivial supermanifold in Proc. Am. Math. Soc. 85, 587-590 (1982; Zbl 0509.58001).
Mathematics Subject Classification ID: 32G05
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 58H15
Mathematics Subject Classification ID: 32K99
zbMATH DE Number: 3935468
zbMATH Keywords: deformation of a complex supermanifold
zbMATH Keywords: Kodaira-Spencer map
zbMATH Keywords: natural generalizations of the Kodaira-Nirenberg-Spencer existence theorems for versal deformations
zbMATH Keywords: superprojective spaces
reviewed by: M. Eastwood
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01077827
OpenAlex ID: W2048583167
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3935468