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 (Artin 1966).
Read more about Rational Singularity: Formulations, Examples
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