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William Fulton in Intersection Theory (1984) writes ... if A and B are subvarieties of a non-singular variety X, the intersection product A · B should be an equivalence class of algebraic cycles closely related to the geometry of how A ∩ B, A and B are situated in X. Two extreme cases have been most familiar.
In 1996 he received the Steele Prize for mathematical exposition for his text Intersection Theory. [1] Fulton is a member of the United States National Academy of Sciences since 1997; a fellow of the American Academy of Arts and Sciences from 1998, and was elected a foreign member of the Royal Swedish Academy of Sciences in 2000. [3]
In mathematics, the Fulton–Hansen connectedness theorem is a result from intersection theory in algebraic geometry, for the case of subvarieties of projective space with codimension large enough to make the intersection have components of dimension at least 1. It is named after William Fulton and Johan Hansen, who proved it in 1979.
For any subvarieties and of a smooth scheme over , with no assumption on the dimension of the intersection, William Fulton and Robert MacPherson's intersection theory constructs a canonical element of the Chow groups of whose image in the Chow groups of is the product [] [].
Let : be a local-complete-intersection morphism that admits a global factorization: it is a composition where is a regular embedding and a smooth morphism. Then the virtual tangent bundle is an element of the Grothendieck group of vector bundles on X given as: [ 5 ]
In algebraic geometry, the scheme-theoretic intersection of closed subschemes X, Y of a scheme W is , the fiber product of the closed immersions,. It is denoted by X ∩ Y {\displaystyle X\cap Y} . Locally, W is given as Spec R {\displaystyle \operatorname {Spec} R} for some ring R and X , Y as Spec ( R / I ) , Spec ( R / J ...
"K-theory and cohomology of algebraic stacks: Riemann-Roch theorems, D-modules and GAGA theorems". arXiv: math/9908097. Lowrey, Parker; Schürg, Timo (2012-08-30). "Grothendieck-Riemann-Roch for derived schemes". arXiv: 1208.6325 . Vakil, Math 245A Topics in algebraic geometry: Introduction to intersection theory in algebraic geometry
In mathematics, a bivariant theory was introduced by Fulton and MacPherson (Fulton & MacPherson 1981), in order to put a ring structure on the Chow group of a singular variety, the resulting ring called an operational Chow ring. On technical levels, a bivariant theory is a mix of a homology theory and a cohomology theory.