English

ALE Calabi-Yau metrics with conical singularities along a compact divisor

Differential Geometry 2021-10-26 v1

Abstract

We construct ALE Calabi-Yau metrics with cone singularities along the exceptional set of resolutions of Cn/Γ\mathbb{C}^n / \Gamma with non-positive discrepancies. In particular, this includes the case of the minimal resolution of two dimensional quotient singularities for any finite subgroup ΓU(2)\Gamma \subset U(2) acting freely on the three-sphere, hence generalizing Kronheimer's construction of smooth ALE gravitational instantons. Finally, we show how our results extend to the more general asymptotically conical setting.

Keywords

Cite

@article{arxiv.1811.12773,
  title  = {ALE Calabi-Yau metrics with conical singularities along a compact divisor},
  author = {Martin de Borbon and Cristiano Spotti},
  journal= {arXiv preprint arXiv:1811.12773},
  year   = {2021}
}