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Given a compact Kähler orbifold with an extremal metric, whose singularities admit a local ALE Kähler scalar-flat resolution, we prove that there exists a Kähler desingularization with an extremal metric. Moreover we study the same problem for constant scalar curvature metrics and prove some partial results.

On the Resolution of Extremal and Constant Scalar Curvature Kähler Orbifolds