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arXiv · 1811.12773

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

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 $\mathbb{C}^n / Γ$ with non-positive discrepancies. In particular, this includes the case of the minimal resolution of two dimensional quotient singularities for any finite subgroup $Γ\subset U(2)$ 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.

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Martin de Borbon, Cristiano Spotti. 2018-11-30. ALE Calabi-Yau metrics with conical singularities along a compact divisor. https://doi.org/10.1093/imrn%2Frnz280

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