Complex supermanifolds of odd dimension beyond 5

Kalus, Matthias

doi:10.1090/proc/13428

Complex supermanifolds of odd dimension beyond 5
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by Matthias Kalus

Proc. Amer. Math. Soc. 145 (2017), 2749-2756

DOI: https://doi.org/10.1090/proc/13428

Published electronically: December 9, 2016

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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 beyond 5 are deduced.

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