Year: 2026
Type: preprint
Abstract: We show that the fundamental group is not locally stable under non-collapsed Gromov--Hausdorff convergence, even among closed Ricci-flat Kähler four-manifolds. More precisely, we construct families of Ricci-flat Kähler metrics on $K3$ surfaces and Enriques surfaces that converge to the same compact flat orbifold. Using the same mechanism, we further construct two families of closed locally hyperkähler Ricci-flat four-manifolds, with fundamental groups $\mathbb Z_2$ and $\mathbb Z_2\times\mathbb Z_2$, respectively, which converge to the same compact flat orbifold.
Source: arXiv (Cornell University)
Authors: Bellati, Alejandro, Bustamante, Ignacio
Institutions: Princeton University, Universidad de la República de Uruguay
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220729812