Deformation of 2-step Nilmanifolds with Abelian Complex Structures

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We develop deformation theory for abelian invariant complex structures on a nilmanifold, and prove that in this case the invariance property is preserved by the Kuranishi process. A purely algebraic condition characterizes the deformations leading again to abelian structures, and we prove that such deformations are unobstructed. Various examples illustrate the resulting theory, and the behavior possible in 3 complex dimensions.

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Differential Geometry, Algebraic Geometry, 32G05; 53C15, 53C56, 57S25, 17B30

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http://salesiana.dossiersoluciones.com/handle/123456789/70067

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0402069
 http://arxiv.org/abs/math/0402069

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arXiv