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We prove an existence theorem for asymptotically conical Ricci‐flat Kähler metrics on    C  2    with cone singularities along a smooth complex curve. These are expected to arise as blow‐up limits of non‐collapsed sequences of Kähler–Einstein metrics with cone singularities.

Asymptotically conical Ricci‐flat Kähler metrics on C 2 with cone singularities along a complex curve