Abstract
Let \(O=(0,0)\) 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.
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This work was supported by the Slovak Research and Development Agency, under the contract No. APVV-16-0053 and by the grant VEGA 1/0596/21.
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Bosáková, A., Chalmovianský, P. (2023). A Note on Local Intersection Multiplicity of Two Plane Curves. In: Cheng, LY. (eds) ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics. ICGG 2022. Lecture Notes on Data Engineering and Communications Technologies, vol 146. Springer, Cham. https://doi.org/10.1007/978-3-031-13588-0_15
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DOI: https://doi.org/10.1007/978-3-031-13588-0_15
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