We show that the deformation space of complex parallelisable nilmanifolds can be described by polynomial equations but is almost never smooth. This is remarkable since these manifolds have trivial canonical bundle and are holomorphic symplectic in even dimension.We describe the Kuranishi space in detail in several examples and also analyse when small deformations remain complex parallelisable.
Cite this article
Sönke Rollenske, The Kuranishi space of complex parallelisable nilmanifolds. J. Eur. Math. Soc. 13 (2011), no. 3, pp. 513–531DOI 10.4171/JEMS/260