Rational Singularity

(Singularity Theory)


Singularity Theory
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What is Rational singularity?

In mathematics, more particularly in the field of algebraic geometry, a scheme has rational singularities, if it is normal, of finite type over a field of characteristic zero, and there exists a proper birational map from a regular scheme such that the higher direct images of applied to are trivial. That is, for . If there is one such resolution, then it follows that all resolutions share this property, since any two resolutions of singularities can be dominated by a third. For surfaces, rational singularities were defined by .

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algebraic surfacesingularity theorysurface


Rational singularities

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