Biholomorphism type of left-invariant complex structures on nilpotent Lie groups

Keizo Hasegawa; Sönke Rollenske; Lorenzo Sillari; Adriano Tomassini; Konstantin Wehler

Biholomorphism type of left-invariant complex structures on nilpotent Lie groups

Differential Geometry 2026-06-30 v1 Algebraic Geometry

Authors: Keizo Hasegawa , Sönke Rollenske , Lorenzo Sillari , Adriano Tomassini , Konstantin Wehler

Abstract

In this note we prove a conjecture by Hasegawa stating that a simply connected, nilpotent Lie group of dimension $2n$ endowed with a left-invariant complex structure is biholomorphic to $\mathbb{C}^n$ .

Cite

@article{arxiv.2606.31448,
  title  = {Biholomorphism type of left-invariant complex structures on nilpotent Lie groups},
  author = {Keizo Hasegawa and Sönke Rollenske and Lorenzo Sillari and Adriano Tomassini and Konstantin Wehler},
  journal= {arXiv preprint arXiv:2606.31448},
  year   = {2026}
}

Comments

6 pages, no figures. Comments are welcome!