On multiplicity of intersection point of two plane algebraic curves

Abstract

The paper studies the multiplicity of intersecting point of two plane algebraic curves. The multiplicity is characterized by means of operators with partial derivatives. It is proved that if A is a point of multiplicity m for one of the curves and, a point of multiplicity n for the other curve, then the arithmetical multiplicity of the intersection (or the number of intersections) of the curves in A, is not less than mn and is equal to mn when the curves do not have common tangents at the point A.