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The Intersection Multiplicity of Intersection Points over Algebraic Curves

Author

Listed:
  • Kailing Lai
  • Fanning Meng
  • Huanqi He
  • Kaiming Zhao

Abstract

In analytic geometry, Bézout’s theorem stated the number of intersection points of two algebraic curves and Fulton introduced the intersection multiplicity of two curves at some point in local case. It is meaningful to give the exact expression of the intersection multiplicity of two curves at some point. In this paper, we mainly express the intersection multiplicity of two curves at some point in R2 and AK2 under fold point, where charK=0. First, we give a sufficient and necessary condition for the coincidence of the intersection multiplicity of two curves at some point and the smallest degree of the terms of these two curves in R2. Furthermore, we show that two different definitions of intersection multiplicity of two curves at a point in AK2 are equivalent and then give the exact expression of the intersection multiplicity of two curves at some point in AK2 under fold point.

Suggested Citation

  • Kailing Lai & Fanning Meng & Huanqi He & Kaiming Zhao, 2023. "The Intersection Multiplicity of Intersection Points over Algebraic Curves," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2023, pages 1-13, May.
    • Handle: RePEc:hin:jijmms:6346685
    DOI: 10.1155/2023/6346685
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