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
Famous quotes containing the words rational and/or singularity:
“Since the Greeks, Western man has believed that Being, all Being, is intelligible, that there is a reason for everything ... and that the cosmos is, finally, intelligible. The Oriental, on the other hand, has accepted his existence within a universe that would appear to be meaningless, to the rational Western mind, and has lived with this meaninglessness. Hence the artistic form that seems natural to the Oriental is one that is just as formless or formal, as irrational, as life itself.”
—William Barrett (b. 1913)
“Losing faith in your own singularity is the start of wisdom, I suppose; also the first announcement of death.”
—Peter Conrad (b. 1948)