Intersection Numbers

Igor R. Shafarevich
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Igor R. Shafarevich: Steklov Mathematical Institute of the Russian Academy of Sciences, Algebra Section

Chapter Chapter 4 in Basic Algebraic Geometry 1, 2013, pp 233-282 from Springer

Abstract: Abstract Taking the intersection of two varieties is an obvious geometric notion. It gives rise to a bilinear multiplication map on algebraic cycles up to linear or algebraic equivalence. A first aim is a rigorous treatment of Bézout’s theorem for the intersection of two curves in the plane. Algebraic cycle class groups and their intersection theory play a role analogous to homology and cohomology in the topology of manifolds. A number of topics are discussed as applications of these ideas, including the adjunction formula for the genus of a curve on a surface, the factorisation of a rational map between nonsingular surfaces into blowups and blowdowns and the classification of Du Val singularities.

Keywords: General Position; Local Ring; Intersection Number; Division Algebra; Local Equation (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-37956-7_4

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DOI: 10.1007/978-3-642-37956-7_4

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