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Intersection Numbers

In: Basic Algebraic Geometry 1

Author

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  • Igor R. Shafarevich

    (Steklov Mathematical Institute)

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.

Suggested Citation

  • Igor R. Shafarevich, 1994. "Intersection Numbers," Springer Books, in: Basic Algebraic Geometry 1, edition 0, chapter 0, pages 223-273, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-57908-0_4
    DOI: 10.1007/978-3-642-57908-0_4
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