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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. 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)
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- 14796 (xsd:nonNegativeInteger)
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- Excess intersection formula (en)
- Jouanolou's key formula (en)
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| rdfs:comment
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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. (en)
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- Residual intersection (en)
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