Stability of abelian complex structures

被引：32

作者：

Console, S

Fino, A

Poon, YS

机构：

[1] Univ Turin, Dipartimento Matemat, I-10128 Turin, Italy

[2] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2006年 / 17卷 / 04期

基金：

美国国家科学基金会;

关键词：

nilmanifold; abelian complex structure; Dolbeault cohomology; Kuranishi deformation;

D O I：

10.1142/S0129167X06003576

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M = Gamma\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 in [7] 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.

引用

页码：401 / 416

页数：16

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