algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

, 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 an ...

''X'' and a

\mathbb

-divisor ''D'' on ''X'' (e.g.,

canonical divisor The adjective canonical is applied in many contexts to mean 'according to the canon' the standard, rule or primary source that is accepted as authoritative for the body of knowledge or literature in that context. In mathematics, ''canonical examp ...

), the discrepancy of the pair (''X'', ''D'') measures the degree of the singularity of the pair.

References

* Algebraic geometry {{Algebraic-geometry-stub

See also

References