Year: 2026
Type: preprint
Abstract: We construct complete ALH hyperkähler metrics on complements of anticanonical elliptic curves with zero self-intersection in smooth rational surfaces. This answers the existence question of Filip--Tosatti, related to the picture proposed by Haskins--Hein--Nordström. Conversely, we prove that every hyperkähler ALH gravitational instanton admits, for each induced complex structure, a compactification by an anticanonical elliptic curve in a rational surface.
Source: arXiv (Cornell University)
Authors: Chen, Yifan, Wei, Chunhui
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214103885