Plane curves meeting at a point with high intersection multiplicity

Abstract

Abstract As a generalization of an inflection point, we consider a point $P$ on a smooth plane curve $C$ of degree $m$ at which another curve $C'$ of degree $n$ meets $C$ with high intersection multiplicity. Especially, we deal with the existence of two curves of degree $m$ and $n$ meeting at the unique point. Keywords : intersection multiplicity, intersection number