Deformation of 2-step Nilmanifolds with Abelian Complex Structures
微分几何
2007-05-23 v1 代数几何
摘要
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.
引用
@article{arxiv.math/0402069,
title = {Deformation of 2-step Nilmanifolds with Abelian Complex Structures},
author = {C. McLaughlin and H. Pedersen and Y. S. Poon and S. Salamon},
journal= {arXiv preprint arXiv:math/0402069},
year = {2007}
}