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arXiv · 2609.26439

ALH Gravitational Instantons and Rational Surfaces

Yifan Chen·Chunhui Wei
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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.

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Yifan Chen, Chunhui Wei. 2026-09-22. ALH Gravitational Instantons and Rational Surfaces. https://arxiv.org/abs/2609.26439

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