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Teichmüller and moduli spaces for complex nilmanifolds

  • Konstantin Wehler
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Abstract

We develop several tools to study the local and global structure of the Teichmüller and moduli spaces for complex nilmanifolds. As a starting point, we prove a structure theorem for holomorphic maps between complex nilmanifolds, which allows for an explicit description of the Teichmüller and moduli spaces. We then introduce two period maps, and give general criteria for the existence of a complex structure on these spaces. To illustrate the theory, we prove a global Torelli theorem for various classes of nilmanifolds, including principal torus bundles over tori and almost abelian nilmanifolds. In particular, we show that there are nilmanifolds of arbitrary dimension and nilpotency index for which the Teichmüller space admits the structure of a complex manifold.

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Cite

BibTeXRIS
BibTeX
@misc{wehler2026teichmüller,
  title = {{Teichmüller and moduli spaces for complex nilmanifolds}},
  author = {Konstantin Wehler},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31516},
  eprint = {2609.31516},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31516},
}
RIS
TY  - UNPB
TI  - Teichmüller and moduli spaces for complex nilmanifolds
AU  - Konstantin Wehler
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31516
UR  - https://arxiv.org/abs/2609.31516
AB  - We develop several tools to study the local and global structure of the Teichmüller and moduli spaces for complex nilmanifolds. As a starting point, we prove a structure theorem for holomorphic maps between complex nilmanifolds, which allows for an explicit description of the Teichmüller and moduli spaces. We then introduce two period maps, and give general criteria for the existence of a complex structure on these spaces. To illustrate the theory, we prove a global Torelli theorem for various classes of nilmanifolds, including principal torus bundles over tori and almost abelian nilmanifolds. In particular, we show that there are nilmanifolds of arbitrary dimension and nilpotency index for which the Teichmüller space admits the structure of a complex manifold.
ER  -