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ALE Ricci-flat Kähler surfaces and weighted projective spaces

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Abstract

We show that the explicit ALE Ricci-flat Kähler metrics constructed by Eguchi–Hanson, Gibbons–Hawking, Hitchin and Kronheimer, and their free quotients are metrics obtained by Tian–Yau techniques. The proof relies on a construction of good compactifications of \(\mathbb {Q}\)-Gorenstein deformations of quotient surface singularities as log del Pezzo surfaces with only cyclic quotient singularities at infinity.

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Acknowledgments

While writing this paper, the second author was partially supported by the NSF Grant DMS-1007114.

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  1. Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville, TN, 37240, USA

    R. Răsdeaconu & I. Şuvaina

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  1. R. Răsdeaconu
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  2. I. Şuvaina
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Correspondence to I. Şuvaina.

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Răsdeaconu, R., Şuvaina, I. ALE Ricci-flat Kähler surfaces and weighted projective spaces. Ann Glob Anal Geom 47, 117–134 (2015). https://doi.org/10.1007/s10455-014-9438-9

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  • DOI: https://doi.org/10.1007/s10455-014-9438-9

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