Complex supermanifolds of odd dimension beyond 5
Complex Variables
2016-01-28 v1
Abstract
Any non-split complex supermanifold is a deformation of a split supermanifold. These deformations are classified by group orbits in a non-abelian cohomology. For the case of a split supermanifold with no global nilpotent even vector fields, an injection of this non-abelian cohomology into an abelian cohomology is constructed. The cochains in the non-abelian complex appear as exponentials of cochains of nilpotent even derivations. Necessary conditions for a recursive construction of these cochains of derivations are analyzed up to terms of degree six. Results on classes of examples of supermanifolds of odd dimension up to 7 are deduced.
Keywords
Cite
@article{arxiv.1601.07434,
title = {Complex supermanifolds of odd dimension beyond 5},
author = {Matthias Kalus},
journal= {arXiv preprint arXiv:1601.07434},
year = {2016}
}