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To give a definition, in the general case, of the intersection multiplicity was the major concern of André Weil's 1946 book Foundations of Algebraic Geometry. Work in the 1920s of B. L. van der Waerden had already addressed the question; in the Italian school of algebraic geometry the ideas were well known, but foundational questions were not ...
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.
encodes all the intersection indices as its coefficients. Witten's conjecture states that the partition function Z = exp F is a τ-function for the KdV hierarchy , in other words it satisfies a certain series of partial differential equations corresponding to the basis { L − 1 , L 0 , L 1 , … } {\displaystyle \{L_{-1},L_{0},L_{1},\ldots ...
Symplectic Floer Homology (SFH) is a homology theory associated to a symplectic manifold and a nondegenerate symplectomorphism of it. If the symplectomorphism is Hamiltonian, the homology arises from studying the symplectic action functional on the (universal cover of the) free loop space of a symplectic manifold.
Schubert calculus is the intersection theory of the 19th century, together with applications to enumerative geometry. Justifying this calculus was the content of Hilbert's 15th problem, and was also the major topic of the 20 century algebraic geometry.
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Intersection theory" The following 13 pages are in this category, out of ...
In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds.It states that if M is an n-dimensional oriented closed manifold (compact and without boundary), then the kth cohomology group of M is isomorphic to the (n − k) th homology group of M, for all integers k
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 ...