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Then the intersection numbers of H and L are given by H 5 =1P, H 4 L=2P, H 3 L 2 =4P, H 2 L 3 =4P, H 1 L 4 =2P, L 5 =1P. So we have (6H−2E) 5 = (2H+2L) 5 = 3264P. Fulton & MacPherson gave a precise description of exactly what "general position" means (although their two propositions about this are not quite right, and are corrected in a note ...
One says that “the affine plane does not have a good intersection theory”, and intersection theory on non-projective varieties is much more difficult. A line on a P 1 × P 1 (which can also be interpreted as the non-singular quadric Q in P 3) has self-intersection 0, since a line can be moved off itself. (It is a ruled surface.)
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The study of moduli spaces of curves, maps and other geometric objects, sometimes via the theory of quantum cohomology. The study of quantum cohomology, Gromov–Witten invariants and mirror symmetry gave a significant progress in Clemens conjecture. Enumerative geometry is very closely tied to intersection theory. [1]
Download as PDF; Printable version; In other projects ... 3264 and All That: A Second Course in Algebraic Geometry, ... William (1998), Intersection Theory, ...
A fundamental issue in algebraic geometry is intersection theory. The Chow ring has many advantages and is widely used. The Chow associated forms give a description of the moduli space of the algebraic varieties in projective space. It gives a beautiful solution of an important problem.
Since André Weil's initial definition of intersection numbers, around 1949, there had been a question of how to provide a more flexible and computable theory, which Serre sought to address. In 1958, Serre realized that classical algebraic-geometric ideas of multiplicity could be generalized using the concepts of homological algebra .
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Intersection theory may refer to: Intersection theory ...