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Mathematics > Differential Geometry

arXiv:1811.12773 (math)
[Submitted on 30 Nov 2018]

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

Authors:Martin de Borbon, Cristiano Spotti
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Abstract:We construct ALE Calabi-Yau metrics with cone singularities along the exceptional set of resolutions of $\mathbb{C}^n / \Gamma$ with non-positive discrepancies. In particular, this includes the case of the minimal resolution of two dimensional quotient singularities for any finite subgroup $\Gamma \subset U(2)$ 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.
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:1811.12773 [math.DG]
  (or arXiv:1811.12773v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1811.12773
Related DOI: https://doi.org/10.1093/imrn/rnz280

Submission history

From: Martin de Borbon MdB [view email]
[v1] Fri, 30 Nov 2018 13:09:11 UTC (19 KB)
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