In
algebraic geometry, given a pair (''X'', ''D'') consisting of a
normal variety In algebraic geometry, an algebraic variety or scheme ''X'' is normal if it is normal at every point, meaning that the local ring at the point is an integrally closed domain. An affine variety ''X'' (understood to be irreducible) is normal if and ...
''X'' and a
-divisor ''D'' on ''X'' (e.g.,
canonical divisor In mathematics, the canonical bundle of a non-singular algebraic variety V of dimension n over a field is the line bundle \,\!\Omega^n = \omega, which is the ''n''th exterior power of the cotangent bundle Ω on ''V''.
Over the complex numbers, it ...
), the discrepancy of the pair (''X'', ''D'') measures the degree of the singularity of the pair.
See also
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Canonical singularity In mathematics, canonical singularities appear as singularities of the canonical model of a projective variety, and terminal singularities are special cases that appear as singularities of minimal models. They were introduced by . Terminal singular ...
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Crepant resolution In algebraic geometry, a crepant resolution of a singularity is a resolution that does not affect the canonical class of the manifold. The term "crepant" was coined by by removing the prefix "dis" from the word "discrepant", to indicate that the ...
References
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Algebraic geometry
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