Abstract

AbstractLet \(O=(0,0)\) be the intersection point of two plane algebraic curves F and G. According to existing results, we know that their intersection multiplicity \(I_O\) at O satisfies the inequality \(I_O(F,G) \ge mn+t\), where m and n are the multiplicities of O on F and G respectively, and t is the number of their common tangents at O (counted with multiplicity). The aim of this paper is to investigate under which conditions the equality occurs. These conditions are given in terms of individual common tangents of F and G at O and their relations to the polynomials defining these curves.KeywordsPlane curvesIntersection multiplicityAlgebraic geometry

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