Intersection theory

Residual intersection

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 . (Wikipedia).

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What is the Alternate Exterior Angle Converse Theorem

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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What is the Corresponding Angle Converse Theorem

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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From playlist Parallel Lines and a Transversal

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What is the Consecutive Interior Angle Converse Theorem

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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Related pages

Scheme-theoretic intersection | Normal cone | Segre class | Bézout's theorem | Euler sequence | Intersection theory | Projective bundle | Projection formula | Chern class | Veronese surface | Steiner's conic problem | Algebraic geometry | Euler class