Suppose that Y is a normal variety such that its canonical class KY is Q-Cartier, and let f:X→Y be a resolution of the singularities of Y.
Then where the sum is over the irreducible exceptional divisors, and the ai are rational numbers, called the discrepancies.
The singularities of a projective variety V are terminal if the variety is normal, some power of the canonical line bundle of the non-singular part of V extends to a line bundle on V, and V the pullback of any section of Vm vanishes along any codimension 1 component of the exceptional locus of a resolution of its singularities.
Two dimensional log terminal singularities are analytically isomorphic to quotients of C2 by finite subgroups of GL2(C).
is a formal linear combination of prime divisors with rational coefficients such that