Intersection Numbers

Igor R. Shafarevich
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Igor R. Shafarevich: Steklov Mathematical Institute

Chapter Chapter IV in Basic Algebraic Geometry 1, 1994, pp 223-273 from Springer

Abstract: Abstract The theorems proved in Chap. I, 6.2 on the dimension of intersection of varieties often allow us to assert that some system of equations has solutions. However, they do not say anything about the number of solutions if this number is finite. The distinction is the same as that between the theorem that roots of a polynomial exist, and the theorem that the number of roots of a polynomial equals its degree. The latter result is only true if we count each root with its multiplicity. In the same way, to state general theorems on the number of points of intersection of varieties, we must assign certain intersection multiplicities to these points. This will be done in the present section.

Keywords: General Position; Prime Ideal; Local Ring; Intersection Number; Local Equation (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-3-642-57908-0_4

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