A solvmanifold with a left-invariant complex structure whose universal cover is not Stein

Shuho Kanda

A solvmanifold with a left-invariant complex structure whose universal cover is not Stein

Differential Geometry 2026-07-08 v1 Complex Variables

Authors: Shuho Kanda

Abstract

We construct a simply connected solvable Lie group $G$ admitting lattices and a left-invariant complex structure $J$ such that $(G,J)$ is not Stein. This provides a counterexample to Hasegawa's conjecture on the Stein property of simply connected unimodular solvable Lie groups with left-invariant complex structures.

Cite

@article{arxiv.2607.07059,
  title  = {A solvmanifold with a left-invariant complex structure whose universal cover is not Stein},
  author = {Shuho Kanda},
  journal= {arXiv preprint arXiv:2607.07059},
  year   = {2026}
}

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5 pages