The Adjunction Formula
Suppose that X is a smooth variety and that D is a smooth divisor on X. The adjunction formula relates the canonical bundles of X and D. It is a natural isomorphism
In terms of canonical classes, it is
This formula is one of the most powerful formulas in algebraic geometry. An important tool of modern birational geometry is inversion of adjunction, which allows one to deduce results about the singularities of X from the singularities of D.
Read more about this topic: Canonical Bundle
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