A Moduli Problem Related to Complex Supermanifolds

A. L. Onishchik ()

A chapter in Algebra and Operator Theory, 1998, pp 13-24 from Springer

Abstract: Abstract We study the problem of classifying complex analytic supermanifolds that have a given retract, i.e., the associated split supermanifold. The problem is solved in the case of the split supermanifold (M, Ω), where M is a simply connected irreducible compact Hermitian symmetric space and Ω the sheaf of holomorphic forms on M. We also give a construction of a family of non-split supermanifolds with retract (M, Ω) for a general complex manifold M. This family is non-empty whenever M is a compact Kähler manifold.

Keywords: Complex Manifold; Open Cover; Cohomology Class; Cotangent Bundle; Holomorphic Vector Bundle (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-011-5072-9_2

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DOI: 10.1007/978-94-011-5072-9_2

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