In
algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
, 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 o ...
''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 model program, minimal models. They were introduced ...
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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 t ...
References
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Algebraic geometry
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