High Quality Content by WIKIPEDIA articles! In mathematics, specifically algebraic geometry, an exceptional divisor for a regular map of varieties is a kind of 'large' subvariety of X which is 'crushed' by f, in a certain definite sense. More strictly, f has an associated exceptional locus which describes how it identifies nearby points in codimension one, and the exceptional divisor is an appropriate algebraic construction whose support is the exceptional locus. The same ideas can be found in the theory of holomorphic mappings of complex manifolds. More precisely, suppose that is a regular map of varieties which is birational (that is, it is an isomorphism between open subsets of X and Y).

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