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Deformation of 2-step nilmanifolds with abelian complex structures

C Maclaughlin Henrik Pedersen Yat Sun Poon Simon Salamon

Differential Geometry mathscidoc:1910.43795

Journal of the London Mathematical Society, 73, (1), 173-193, 2006.2
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 three complex dimensions.
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@inproceedings{c2006deformation,
  title={Deformation of 2-step nilmanifolds with abelian complex structures},
  author={C Maclaughlin, Henrik Pedersen, Yat Sun Poon, and Simon Salamon},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020220456163631324},
  booktitle={Journal of the London Mathematical Society},
  volume={73},
  number={1},
  pages={173-193},
  year={2006},
}
C Maclaughlin, Henrik Pedersen, Yat Sun Poon, and Simon Salamon. Deformation of 2-step nilmanifolds with abelian complex structures. 2006. Vol. 73. In Journal of the London Mathematical Society. pp.173-193. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020220456163631324.
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