About: Residual intersection

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In algebraic geometry, the problem of residual intersection asks the following: Given a subset Z in the intersection of varieties, understand the complement of Z in the intersection; i.e., the residual set to Z. The intersection determines a class , the intersection product, in the Chow group of an ambient space and, in this situation, the problem is to understand the class, the residual class to Z: where means the part supported on Z; classically the degree of the part supported on Z is called the equivalence of Z.

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rdf:type	Thing
rdfs:label	Residual intersection (en)
rdfs:comment	In algebraic geometry, the problem of residual intersection asks the following: Given a subset Z in the intersection of varieties, understand the complement of Z in the intersection; i.e., the residual set to Z. The intersection determines a class , the intersection product, in the Chow group of an ambient space and, in this situation, the problem is to understand the class, the residual class to Z: where means the part supported on Z; classically the degree of the part supported on Z is called the equivalence of Z. (en)
rdfs:seeAlso	Steiner's conic problem
name	Excess intersection formula (en) Jouanolou's key formula (en)
dcterms:subject	Intersection theory
Wikipage page ID	54145380 (xsd:integer)
Wikipage revision ID	1074177831 (xsd:integer)
Link from a Wikipage to another Wikipage	Projection formula Projective bundle Chow ring Normal cone Ergebnisse der Mathematik und ihrer Grenzgebiete Bézout's theorem Algebraic geometry Intersection theory Advances in Mathematics Chern class Intersection theory Euler class Euler sequence Scheme-theoretic intersection Segre class Veronese surface Steiner's conic problem Intersection product Springer-Verlag First Chern class Complete intersection morphism dbr:Infinitesimally_close dbr:Multiple-point_formula dbr:Self-intersection_formula
Link from a Wikipage to an external page	https://kluedo.ub.uni-kl.de/frontdoor/deliver/index/docId/3750/file/Hiep_Dang_thesis.pdf
sameAs	Residual intersection Residual intersection
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has abstract	In algebraic geometry, the problem of residual intersection asks the following: Given a subset Z in the intersection of varieties, understand the complement of Z in the intersection; i.e., the residual set to Z. The intersection determines a class , the intersection product, in the Chow group of an ambient space and, in this situation, the problem is to understand the class, the residual class to Z: where means the part supported on Z; classically the degree of the part supported on Z is called the equivalence of Z. The two principal applications are the solutions to problems in enumerative geometry (e.g., Steiner's conic problem) and the derivation of the , the formula allowing one to count or enumerate the points in a fiber even when they are . The problem of residual intersection goes back to the 19th century. The modern formulation of the problems and the solutions is due to Fulton and MacPherson. To be precise, they develop the intersection theory by a way of solving the problems of residual intersections (namely, by the use of the Segre class of a normal cone to an intersection.) A generalization to a situation where the assumption on regular embedding is weakened is due to . (en)
math statement	. (en)
prov:wasDerivedFrom	wikipedia-en:Residual_intersection?oldid=1074177831&ns=0
page length (characters) of wiki page	14796 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Residual_intersection
is Link from a Wikipage to another Wikipage of	Normal cone Segre class
is foaf:primaryTopic of	wikipedia-en:Residual_intersection

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