A singular point on a normal two-dimensional algebraic variety has an integrally closed local domain which is not a regular local ring. A rational double point is an important isolated example with a crepant minimal resolution.
A rational double point is a normal surface singularity whose minimal resolution has a configuration of smooth rational -curves of type , or . Birational projective models of K3 surfaces arising from nef big systems contract orthogonal -curves to these singularities.
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