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- Exceptional_divisor abstract "In mathematics, specifically algebraic geometry, an exceptional divisor for a regular map of varieties is a kind of 'large' subvariety of which is 'crushed' by , 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 and ). A codimension-1 subvariety is said to be exceptional if has codimension at least 2 as a subvariety of . One may then define the exceptional divisor of to be where the sum is over all exceptional subvarieties of , and is an element of the group of Weil divisors on .Consideration of exceptional divisors is crucial in birational geometry: an elementary result (see for instance Shafarevich, II.4.4) shows that any birational regular map that is not an isomorphism has an exceptional divisor. A particularly important example is the blowup of a subvariety in this case the exceptional divisor is exactly the preimage of .".
- Exceptional_divisor wikiPageID "14271694".
- Exceptional_divisor wikiPageRevisionID "575620526".
- Exceptional_divisor hasPhotoCollection Exceptional_divisor.
- Exceptional_divisor subject Category:Algebraic_geometry.
- Exceptional_divisor subject Category:Birational_geometry.
- Exceptional_divisor comment "In mathematics, specifically algebraic geometry, an exceptional divisor for a regular map of varieties is a kind of 'large' subvariety of which is 'crushed' by , 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.".
- Exceptional_divisor label "Exceptional divisor".
- Exceptional_divisor sameAs m.03czv19.
- Exceptional_divisor sameAs Q5419508.
- Exceptional_divisor sameAs Q5419508.
- Exceptional_divisor wasDerivedFrom Exceptional_divisor?oldid=575620526.
- Exceptional_divisor isPrimaryTopicOf Exceptional_divisor.