Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.09026 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Let $X$ be a smooth quasi-projective variety. Assume that the (topological) fundamental group $π_1(X, x)$ is torsion-free nilpotent. We show that if the first Betti number $b_1(X) \le 3$, then $π_1(X, x)$ is isomorphic to either $\mathbb{Z}^n$ for $n = 1, 2, 3$, a lattice in the Heisenberg group $H_3(\mathbb{R})$ or $\mathbb{R} \times H_3(\mathbb{R})$. Moreover, we prove that $π_1(X, x)$ is abelian or $2$-step nilpotent if its rank is less than or equal to seven. More precisely, we determine the real nilpotent Lie groups in which torsion-free nilpotent fundamental groups can be embedded as lattices for ranks up to six and seven, respectively. Our main results are a partial positive answer to a question on nilpotent (quasi-)Kähler groups posed by Aguilar and Campana.