PreprintarXiv licencearXiv
ALH Gravitational Instantons and Rational Surfaces
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.
Related
- Gravitational instantons and hyperbolic space
- The twistor construction of toric gravitational instantons
- On the Geroch conjecture for toric gravitational instantons
- Pure Spinor Factorization of Belinski-Zakharov Solitons and Regular Gravitational Instantons
- Stability of gravitational instantons with a bounded Killing vector field
BibTeX
@misc{chen2026gravitational,
title = {{ALH Gravitational Instantons and Rational Surfaces}},
author = {Yifan Chen and Chunhui Wei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26439},
eprint = {2609.26439},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26439},
}
RIS
TY - UNPB
TI - ALH Gravitational Instantons and Rational Surfaces
AU - Yifan Chen
AU - Chunhui Wei
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26439
UR - https://arxiv.org/abs/2609.26439
AB - 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.
ER -