About: Intersection theory

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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. 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 definitive form. There is yet an ongoing development of intersection theory. Currently the main focus is on: virtual fundamental cycles, quantum intersection rings, Gromov-Witten theory and the extension of intersection theory from schemes to stacks.

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rdf:type	Thing organisation
rdfs:label	Intersection theory (en) Teoria dell'intersezione (it) 交叉理論 (ja)
rdfs:comment	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. 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 definitive form. There is yet an ongoing development of intersection theory. Currently the main focus is on: virtual fundamental cycles, quantum intersection rings, Gromov-Witten theory and the extension of intersection theory from schemes to stacks. (en) 数学では、交叉理論(intersection theory)（もしくは、交点理論）は、代数幾何学では代数多様体の上ので部分多様体の交叉についての分野で、代数トポロジーではコホモロジー環の中の交叉の計算についての分野である。多様体の理論は古くからあり、曲線のベズーの定理や(elimination theory)に起源を持つ。他方、トポロジー理論では、交叉理論はより手短に定義形式へたどり着く。 (ja) In matematica, e più in particolare in geometria, con il termine teoria dell'intersezione, o anche con teoria dell'intersezione geometrica, si intende lo studio delle intersezioni fra varietà algebriche. Essa si può considerare una parte della , parte della geometria algebrica che si occupa di contare oggetti geometrici di tipo ben definito e soggetti a restrizioni esprimibili con equazioni che rendono finito il numero degli oggetti stessi. La teoria dell'intersezione ha quindi forti collegamenti anche con la odierna combinatorica enumerativa. (it)
differentFrom	Intersection (set theory) Intersectionality
rdfs:seeAlso	Ε-quadratic form
foaf:depiction
dcterms:subject	Intersection theory
Wikipage page ID	3148602 (xsd:integer)
Wikipage revision ID	1087131685 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective plane Quadric Elimination theory Enumerative geometry Minimal model (birational geometry) dbr:Bartel_Leendert_van_der_Waerden Bilinear form Algebraic cycle Algebraic surface Cup product Intersection Topological invariant Compact space Mathematics Chow ring Generic point Normal bundle Connected space Ergebnisse der Mathematik und ihrer Grenzgebiete André Weil Chow group Function field of an algebraic variety Fundamental class Stack (mathematics) Bézout's theorem William Fulton (mathematician) Linear system of divisors Poincaré duality Algebraic geometry Alternating form 4-manifold Italian school of algebraic geometry Length of a module Quadratic form Regular local ring Guido Castelnuovo Intersection form (4-manifold) Jean-Pierre Serre Chern class Birational geometry Blowing up Codimension Homeomorphism Tor functor Symmetric bilinear form Intersection theory Spectral sequence Grothendieck–Riemann–Roch theorem Michael Freedman Orientability Castelnuovo's contraction theorem Morphism of schemes Signature (topology) Euclidean plane Ruled surface Ε-quadratic form Intersection multiplicity Equivalence relations on algebraic cycles Simply connected Springer-Verlag Framed manifold Doubly even Gromov-Witten theory Singly even Cohomology group Dimension of a manifold Ε-symmetric form Subvarieties dbr:Oriented_intersection_number
Link from a Wikipage to an external page	http://www.mathematik.uni-kl.de/agag/mitglieder/professoren/gathmann/notes/alggeom/ http://www.math.uni-bonn.de/people/tian/Intersection-theory.pdf https://web.archive.org/web/20160521223954/http:/www.mathematik.uni-kl.de/agag/mitglieder/professoren/gathmann/notes/alggeom/
sameAs	Intersection theory Intersection theory Intersection theory Intersection theory Intersection theory
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