Stability of Abelian Complex Structures

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Let $M = Γ\backslash G$ be a nilmanifold endowed with an invariant complex structure. We prove that Kuranishi deformations of abelian complex structures are all invariant complex structures, generalizing a result of C. Maclaughlin, H. Pedersen, Y.S. Poon and S. Salamon for 2-step nilmanifolds. We characterize small deformations that remain abelian. As an application, we observe that at real dimension six, the deformation process of abelian complex structures is stable within the class of nilpotent complex structures. We give an example to show that this property does not hold in higher dimension.
17 pages

Keywords

Differential Geometry, Algebraic Geometry, 32G05; 53C15; 53C56; 57S25; 22E25

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/75506

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506314
 http://arxiv.org/abs/math/0506314

Collections

arXiv