Let M 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 previous result 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.

Stability of Abelian Complex Structures

CONSOLE, Sergio;FINO, Anna Maria;
2006-01-01

Abstract

Let M 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 previous result 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.
2006
17
401
416
Nilmanifold; abelian complex structure; Dolbeault cohomology Kuranishi 23 deformation.
S. Console; A. Fino; Y.S. Poon
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/22393
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