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A Moduli Problem Related to Complex Supermanifolds

In: Algebra and Operator Theory

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  • A. L. Onishchik

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.

Suggested Citation

  • A. L. Onishchik, 1998. "A Moduli Problem Related to Complex Supermanifolds," Springer Books, in: Yusupdjan Khakimdjanov & Michel Goze & Shavkat A. Ayupov (ed.), Algebra and Operator Theory, pages 13-24, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5072-9_2
    DOI: 10.1007/978-94-011-5072-9_2
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