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In mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. [1] The theory for varieties is older, with roots in Bézout's theorem on curves and elimination theory. On the other hand, the topological theory more quickly reached a ...
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Many recent academics, such as Leslie McCall, have argued that the introduction of the intersectionality theory was vital to sociology and that before the development of the theory, there was little research that specifically addressed the experiences of people who are subjected to multiple forms of oppression within society.
Intersection homology was originally defined on suitable spaces with a stratification, though the groups often turn out to be independent of the choice of stratification. There are many different definitions of stratified spaces. A convenient one for intersection homology is an n-dimensional topological pseudomanifold.
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 ...
Fulton and MacPherson extended the Chow ring to singular varieties by defining the "operational Chow ring" and more generally a bivariant theory associated to any morphism of schemes. [13] A bivariant theory is a pair of covariant and contravariant functors that assign to a map a group and a ring respectively.
"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
The second potential problem is that even if the intersection is zero-dimensional, it may be non-transverse, for example, if V is a plane curve and W is one of its tangent lines. The first problem requires the machinery of intersection theory, discussed above in detail, which replaces V and W by more convenient subvarieties using the moving lemma.